Axioms

17 pages, 344 KiB

Open AccessArticle

On the Conflation of Poisson and Logarithmic Distributions with Applications

by Abdulhamid A. Alzaid, Anfal A. Alqefari and Najla Qarmalah

Axioms 2025, 14(7), 518; https://doi.org/10.3390/axioms14070518 (registering DOI) - 6 Jul 2025

It is frequent for real-life count data to show inflation in lower values; however, most of the well-known count distributions cannot capture such a feature. The present paper introduces a new distribution for modeling inflated count data in small values based on a [...] Read more.

It is frequent for real-life count data to show inflation in lower values; however, most of the well-known count distributions cannot capture such a feature. The present paper introduces a new distribution for modeling inflated count data in small values based on a conflation of distributions approach. The new distribution inherits some properties from Poisson distribution (PD) and logarithmic distribution (LD), making it a powerful modeling tool. It can serve as an alternative to PD, LD, and zero-truncated distributions. The new distribution is worth considering theoretically, as it belongs to the weighted PD family. With zero as a support point, two additional models are suggested for the new distribution. These modifications yield distributions that demonstrate overdispersion models comparable to the negative binomial distribution (NBD) while retaining essential PD properties, making them suitable for accurately representing count data with frequent events of low frequency and high variance. Furthermore, we discuss the superior performance of three new distributions in modeling real count data compared to traditional count distributions such as PD and NBD, as well as other discrete distributions. This paper examines the key statistical properties of the proposed distributions. A comparison of the novel and other distributions in the literature is shown employing real-life data from some domains. All of the computations shown in this study are generated using the R programming language. Full article

(This article belongs to the Special Issue Advances in the Theory and Applications of Statistical Distributions)

12 pages, 265 KiB

Open AccessArticle

Existence of Weakly Pareto–Nash Equilibrium for Multiobjective Games with Infinitely Many Players

by Huaxin Chen and Wensheng Jia

Axioms 2025, 14(7), 517; https://doi.org/10.3390/axioms14070517 (registering DOI) - 4 Jul 2025

Abstract

Our work proves the existence of weakly Pareto–Nash equilibrium (PNE) in multiobjective games (MGs) with infinitely many players. First, we demonstrate the existence of weakly PNE under compactness assumptions by using the intersection theorem. Then, we extend the intersection theorem to the non-compact [...] Read more.

Our work proves the existence of weakly Pareto–Nash equilibrium (PNE) in multiobjective games (MGs) with infinitely many players. First, we demonstrate the existence of weakly PNE under compactness assumptions by using the intersection theorem. Then, we extend the intersection theorem to the non-compact case and obtain a new intersection theorem. Finally, we prove the existence of weakly PNE in MGs with infinitely many players without compactness assumptions. Full article

(This article belongs to the Special Issue Mathematical Optimizations and Operations Research)

25 pages, 646 KiB

Open AccessArticle

Exponential Squared Loss-Based Robust Variable Selection with Prior Information in Linear Regression Models

by Hejun Wei, Tian Jin and Yunquan Song

Axioms 2025, 14(7), 516; https://doi.org/10.3390/axioms14070516 (registering DOI) - 4 Jul 2025

Abstract

This paper proposes a robust variable selection method that incorporates prior information through linear constraints. For more than a decade, penalized likelihood frameworks have been the predominant approach for variable selection, where appropriate loss and penalty functions are selected to formulate unconstrained optimization [...] Read more.

This paper proposes a robust variable selection method that incorporates prior information through linear constraints. For more than a decade, penalized likelihood frameworks have been the predominant approach for variable selection, where appropriate loss and penalty functions are selected to formulate unconstrained optimization problems. However, in many specific applications, some prior information can be obtained. In this paper, we reformulate variable selection by incorporating prior knowledge as linear constraints. In addition, the loss function adopted in this paper is a robust exponential squared loss function, which ensures that the estimation of model parameter coefficient will not have a great impact when there are a few outliers in the dataset. This paper uses the designed solution algorithm to calculate the estimated values of coefficients and some other parameters, and finally conducts numerical simulations and a real-data experiment. Experimental results demonstrate that our model significantly improves estimation robustness compared to existing methods, even in outlier-contaminated scenarios. Full article

(This article belongs to the Special Issue Computational Statistics and Its Applications, 2nd Edition)

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21 pages, 1556 KiB

Open AccessArticle

Hexic-Chebyshev Collocation Method for Solving Distributed-Order Time-Space Fractional Diffusion Equations

by Afshin Babaei, Sedigheh Banihashemi, Behrouz Parsa Moghaddam and Arman Dabiri

Axioms 2025, 14(7), 515; https://doi.org/10.3390/axioms14070515 - 3 Jul 2025

Abstract

This paper presents a spectral method to solve nonlinear distributed-order diffusion equations with both time-distributed-order and two-sided space-fractional terms. These are highly challenging to solve analytically due to the interplay between nonlinearity and the fractional distributed-order nature of the time and space derivatives. [...] Read more.

This paper presents a spectral method to solve nonlinear distributed-order diffusion equations with both time-distributed-order and two-sided space-fractional terms. These are highly challenging to solve analytically due to the interplay between nonlinearity and the fractional distributed-order nature of the time and space derivatives. For this purpose, Hexic-kind Chebyshev polynomials (HCPs) are used as the backbone of the method to transform the primary problem into a set of nonlinear algebraic equations, which can be efficiently solved using numerical solvers, such as the Newton–Raphson method. The primary reason of choosing HCPs is due to their remarkable recurrence relations, facilitating their efficient computation and manipulation in mathematical analyses. A comprehensive convergence analysis was conducted to validate the robustness of the proposed method, with an error bound derived to provide theoretical guarantees for the solution’s accuracy. The method’s effectiveness is further demonstrated through two test examples, where the numerical results are compared with existing solutions, confirming the approach’s accuracy and reliability. Full article

(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inequalities)

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22 pages, 753 KiB

Open AccessArticle

Existence and Global Exponential Stability of Equilibrium for an Epidemic Model with Piecewise Constant Argument of Generalized Type

by Kuo-Shou Chiu and Fernando Córdova-Lepe

Axioms 2025, 14(7), 514; https://doi.org/10.3390/axioms14070514 - 3 Jul 2025

Abstract

The authors investigate an epidemic model described by a differential equation, which includes a piecewise constant argument of the generalized type (DEPCAG). In this work, the main goal is to find an invariant region for the system and prove the existence and uniqueness [...] Read more.

The authors investigate an epidemic model described by a differential equation, which includes a piecewise constant argument of the generalized type (DEPCAG). In this work, the main goal is to find an invariant region for the system and prove the existence and uniqueness of solutions with the defined conditions using integral equations. On top of that, an auxiliary result is established, outlining the relationship between the unknown function values in the deviation argument and the time parameter. The stability analysis is conducted using the Lyapunov–Razumikhin method, adapted for differential equations with a piecewise constant argument of the generalized type. The trivial equilibrium’s stability is examined, and the stability of the positive equilibrium is assessed by transforming it into a trivial form. Finally, sufficient conditions for the uniform asymptotic stability of both the trivial and positive equilibria are established. Full article

(This article belongs to the Section Mathematical Analysis)

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17 pages, 3336 KiB

Open AccessArticle

Modeling and Exploration of Localized Wave Phenomena in Optical Fibers Using the Generalized Kundu–Eckhaus Equation for Femtosecond Pulse Transmission

by Ejaz Hussain, Ali H. Tedjani, Khizar Farooq and Beenish

Axioms 2025, 14(7), 513; https://doi.org/10.3390/axioms14070513 - 3 Jul 2025

Abstract

This manuscript aims to explore localized waves for the nonlinear partial differential equation referred to as the

(1 + 1)

-dimensional generalized Kundu–Eckhaus equation with an additional dispersion term that describes the propagation of the ultra-short femtosecond pulses in an optical [...] Read more.

This manuscript aims to explore localized waves for the nonlinear partial differential equation referred to as the

(1 + 1)

-dimensional generalized Kundu–Eckhaus equation with an additional dispersion term that describes the propagation of the ultra-short femtosecond pulses in an optical fiber. This research delves deep into the characteristics, behaviors, and localized waves of the

(1 + 1)

-dimensional generalized Kundu–Eckhaus equation. We utilize the multivariate generalized exponential rational integral function method (MGERIFM) to derive localized waves, examining their properties, including propagation behaviors and interactions. Motivated by the generalized exponential rational integral function method, it proves to be a powerful tool for finding solutions involving the exponential, trigonometric, and hyperbolic functions. The solutions we found using the MGERIF method have important applications in different scientific domains, including nonlinear optics, plasma physics, fluid dynamics, mathematical physics, and condensed matter physics. We apply the three-dimensional (3D) and contour plots to illuminate the physical significance of the derived solution, exploring the various parameter choices. The proposed approaches are significant and applicable to various nonlinear evolutionary equations used to model nonlinear physical systems in the field of nonlinear sciences. Full article

(This article belongs to the Special Issue Applied Nonlinear Dynamical Systems in Mathematical Physics)

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11 pages, 260 KiB

Open AccessArticle

Averaging of Linear Quadratic Parabolic Optimal Control Problem

by Olena Kapustian, Oleksandr Laptiev and Adalbert Makarovych

Axioms 2025, 14(7), 512; https://doi.org/10.3390/axioms14070512 - 2 Jul 2025

Abstract

This paper studies an averaged Linear Quadratic Regulator (LQR) problem for a parabolic partial differential equation (PDE), where the system dynamics are affected by uncertain parameters. Instead of assuming a deterministic operator, we model the uncertainty using a probability distribution over a set [...] Read more.

This paper studies an averaged Linear Quadratic Regulator (LQR) problem for a parabolic partial differential equation (PDE), where the system dynamics are affected by uncertain parameters. Instead of assuming a deterministic operator, we model the uncertainty using a probability distribution over a set of possible system dynamics. This approach extends classical optimal control theory by incorporating an averaging framework to account for parameter uncertainty. We establish the existence and uniqueness of the optimal control solution and analyze its convergence as the probability distribution governing the system parameters changes. These results provide a rigorous foundation for solving optimal control problems in the presence of parameter uncertainty. Our findings lay the groundwork for further studies on optimal control in dynamic systems with uncertainty. Full article

(This article belongs to the Special Issue Modern Trends and Application of Decision-Making Theory, Stability and Control)

20 pages, 1115 KiB

Open AccessArticle

A Novel Computational Framework for Time-Fractional Higher-Order KdV Models: CLADM-Based Solutions and Comparative Analysis

by Priti V. Tandel, Anant Patel and Trushitkumar Patel

Axioms 2025, 14(7), 511; https://doi.org/10.3390/axioms14070511 - 1 Jul 2025

Abstract

This study applies the Conformable Laplace Adomian Decomposition Method (CLADM) to solve generalized time-fractional Korteweg–de Vries (KdV) models, including seventh- and fifth-order models. CLADM combines the conformable fractional derivative and Laplace transform with the Adomian decomposition technique, offering analytic approximate solutions. Numerical and [...] Read more.

This study applies the Conformable Laplace Adomian Decomposition Method (CLADM) to solve generalized time-fractional Korteweg–de Vries (KdV) models, including seventh- and fifth-order models. CLADM combines the conformable fractional derivative and Laplace transform with the Adomian decomposition technique, offering analytic approximate solutions. Numerical and graphical results, generated using MATLAB R2020a 9.8.0.1323502, validate the method’s efficiency and precision in capturing fractional-order dynamics. Fractional parameters

ϱ

significantly influence wave behavior, with higher orders yielding smoother profiles and reduced oscillations. Comparative analysis confirms CLADM’s superiority over existing methods in minimizing errors. The versatility of CLADM highlights its potential for studying nonlinear wave phenomena in diverse applications. Full article

(This article belongs to the Special Issue Fractional Calculus and Applied Analysis, 2nd Edition)

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59 pages, 1417 KiB

Open AccessArticle

Symmetrized Neural Network Operators in Fractional Calculus: Caputo Derivatives, Asymptotic Analysis, and the Voronovskaya–Santos–Sales Theorem

by Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales and Gislan Silveira Santos

Axioms 2025, 14(7), 510; https://doi.org/10.3390/axioms14070510 - 30 Jun 2025

Abstract

This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for [...] Read more.

This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for three classes of multivariate operators: quasi-interpolation, Kantorovich-type, and quadrature-type. A central theoretical contribution is the derivation of the Voronovskaya–Santos–Sales Theorem, which extends classical asymptotic expansions to the fractional domain, providing rigorous error bounds and normalized remainder terms governed by Caputo derivatives. The operators exhibit key properties such as partition of unity, exponential decay, and scaling invariance, which are essential for stable and accurate approximations in high-dimensional settings and systems governed by nonlocal dynamics. The theoretical framework is thoroughly validated through applications in signal processing and fractional fluid dynamics, including the formulation of nonlocal viscous models and fractional Navier–Stokes equations with memory effects. Numerical experiments demonstrate a relative error reduction of up to 92.5% when compared to classical quasi-interpolation operators, with observed convergence rates reaching

O (n^{- 1.5})

under Caputo derivatives, using parameters

λ = 3.5

,

q = 1.8

, and

n = 100

. This synergy between neural operator theory, asymptotic analysis, and fractional calculus not only advances the theoretical landscape of function approximation but also provides practical computational tools for addressing complex physical systems characterized by long-range interactions and anomalous diffusion. Full article

(This article belongs to the Special Issue Advances in Fuzzy Logic and Computational Intelligence)

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18 pages, 271 KiB

Open AccessArticle

New Results on Idempotent Operators in Hilbert Spaces

by Salma Aljawi, Cristian Conde, Kais Feki and Shigeru Furuichi

Axioms 2025, 14(7), 509; https://doi.org/10.3390/axioms14070509 - 30 Jun 2025

Abstract

This paper provides a new proof of the operator norm identity

∥ Q ∥ = ∥ I - Q ∥

, where Q is a bounded idempotent operator on a complex Hilbert space, and I is the identity operator. We also [...] Read more.

This paper provides a new proof of the operator norm identity

∥ Q ∥ = ∥ I - Q ∥

, where Q is a bounded idempotent operator on a complex Hilbert space, and I is the identity operator. We also derive explicit lower and upper bounds for the distance from an arbitrary idempotent operator to the set of orthogonal projections. Our approach simplifies existing proofs. Full article

(This article belongs to the Section Mathematical Analysis)

18 pages, 361 KiB

Open AccessArticle

Analyzing Competing Risks with Progressively Type-II Censored Data in Dagum Distributions

by Raghd Badwan and Reza Pakyari

Axioms 2025, 14(7), 508; https://doi.org/10.3390/axioms14070508 - 30 Jun 2025

Abstract

Competing risk models are essential in survival analysis for studying systems with multiple mutually exclusive failure events. This study investigates the application of competing risk models in the presence of progressively Type-II censored data for the Dagum distribution, a flexible distribution suited for [...] Read more.

Competing risk models are essential in survival analysis for studying systems with multiple mutually exclusive failure events. This study investigates the application of competing risk models in the presence of progressively Type-II censored data for the Dagum distribution, a flexible distribution suited for modeling data with heavy tails and varying skewness and kurtosis. The methodology includes maximum likelihood estimation of the unknown parameters, with a focus on the special case of a common shape parameter, which allows for a closed-form expression of the relative risks. A hypothesis test is developed to assess the validity of this assumption, and both asymptotic and bootstrap confidence intervals are constructed. The performance of the proposed methods is evaluated through Monte Carlo simulations, and their applicability is demonstrated with a real-world example. Full article

(This article belongs to the Special Issue Recent Stochastic and Statistical Approaches for Modeling Complex Systems and Dependent Variables)

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21 pages, 565 KiB

Open AccessArticle

Transfer Learning of High-Dimensional Stochastic Frontier Model via Elastic Net

by Jiahao Chen, Wenjun Chen and Yunquan Song

Axioms 2025, 14(7), 507; https://doi.org/10.3390/axioms14070507 - 28 Jun 2025

Abstract

In this paper, the high-dimensional stochastic frontier model problem is explored via Elastic Net under the transfer learning framework. When the target data is limited, transfer learning improves the accuracy of model estimation and prediction by transferring the source data. When the transferable [...] Read more.

In this paper, the high-dimensional stochastic frontier model problem is explored via Elastic Net under the transfer learning framework. When the target data is limited, transfer learning improves the accuracy of model estimation and prediction by transferring the source data. When the transferable source is known, a transfer learning algorithm for a high-dimensional stochastic frontier model is proposed based on Elastic Net. In addition, based on the prior knowledge of the parameters, this paper introduces linear constraints to improve the estimation accuracy in transfer learning. When the transferable source is unknown, this paper designs a corresponding algorithm to detect the transferable source. Finally, the effectiveness of the method is proved by simulation experiments and actual cases. Full article

(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 2nd Edition)

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17 pages, 322 KiB

Open AccessArticle

A New Class of (α,η,(Q,h),L)-Contractions in Triple Controlled Metric-Type Spaces with Application to Polynomial Sine-Type Equations

by Fatima M. Azmi

Axioms 2025, 14(7), 506; https://doi.org/10.3390/axioms14070506 - 27 Jun 2025

Abstract

This paper introduces a novel class of generalized contractions, termed

(α, η, (Q, h), L)

-contraction mapping, within the context of triple controlled metric-type spaces, extending the framework of fixed point theory in controlled structures. [...] Read more.

This paper introduces a novel class of generalized contractions, termed

(α, η, (Q, h), L)

-contraction mapping, within the context of triple controlled metric-type spaces, extending the framework of fixed point theory in controlled structures. The proposed mapping is defined using

α

-admissible and

η

-subadmissible functions, in conjunction with a control pair

(Q, h)

of upper class of type I, and incorporates Wardowski’s function

L

-contraction condition. Under suitable hypotheses, we establish both the existence and uniqueness of fixed points for this class of mappings. Several corollaries are derived as special cases of the main result. Moreover, we provide a nontrivial application by analyzing the solvability of a nonlinear equation involving powers of the sine function, thereby illustrating the utility of the developed theory. Full article

(This article belongs to the Section Mathematical Analysis)

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23 pages, 1675 KiB

Open AccessArticle

H_∞ Preview Tracking Control of Time-Delay Discrete Systems and Its Application in Nuclear Reactor Problems

by Fucheng Liao, Hao Xie, Xianchun Meng, Jiang Wu, Yucheng Wei and Jiamei Deng

Axioms 2025, 14(7), 505; https://doi.org/10.3390/axioms14070505 - 27 Jun 2025

Abstract

Improving the tracking accuracy and effectiveness of the pressurizer control system with respect to the reference signal is an effective method to enhance the safe and stable operation of nuclear reactors. This paper applies preview tracking control to the pressurizer control system. For [...] Read more.

Improving the tracking accuracy and effectiveness of the pressurizer control system with respect to the reference signal is an effective method to enhance the safe and stable operation of nuclear reactors. This paper applies preview tracking control to the pressurizer control system. For the simplified control system model of the pressurizer, we first study its general structure, which can be characterized as a discrete-time system with state delay. Unlike conventional control systems, the system considered in this study features control inputs that are represented as cumulative sums of historical inputs. In order to design a preview tracking controller for such systems, we adopt the difference method and state augmentation technique and introduce an equality containing the reference signal and a discrete integrator to construct an augmented error system. Simultaneously, a performance signal is defined to evaluate the impact of external disturbances on system performance. Thus, the preview tracking control problem of the original system is reformulated as an

H_{\infty}

control problem for the augmented error system. Subsequently, a memory-based state feedback controller is designed for the augmented error system. Then, by employing the Lyapunov function and linear matrix inequality (LMI), the

H_{\infty}

preview tracking controller for the original system is derived. Finally, the proposed control strategy is applied to a pressurizer control system model, and numerical simulations are conducted to validate the effectiveness of the proposed controller by using MATLAB (R2023a, MathWorks, Natick, MA, USA). Full article

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22 pages, 670 KiB

Open AccessArticle

LDC-GAT: A Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware Optimization

by Liping Chen, Hongji Zhu and Shuguang Han

Axioms 2025, 14(7), 504; https://doi.org/10.3390/axioms14070504 - 27 Jun 2025

Abstract

Graph attention networks are pivotal for modeling non-Euclidean data, yet they face dual challenges: training oscillations induced by projection-based high-dimensional constraints and gradient anomalies due to poor adaptation to heterophilic structure. To address these issues, we propose LDC-GAT (Lyapunov-Stable Graph Attention Network with [...] Read more.

Graph attention networks are pivotal for modeling non-Euclidean data, yet they face dual challenges: training oscillations induced by projection-based high-dimensional constraints and gradient anomalies due to poor adaptation to heterophilic structure. To address these issues, we propose LDC-GAT (Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware Optimization), which jointly optimizes both forward and backward propagation processes. In the forward path, we introduce Dynamic Residual Graph Filtering, which integrates a tunable self-loop coefficient to balance neighborhood aggregation and self-feature retention. This filtering mechanism, constrained by a lower bound on Dirichlet energy, improves multi-head attention via multi-scale fusion and mitigates overfitting. In the backward path, we design the Fro-FWNAdam, a gradient descent algorithm guided by a learning-rate-aware perceptron. An explicit Frobenius norm bound on weights is derived from Lyapunov theory to form the basis of the perceptron. This stability-aware optimizer is embedded within a Frank–Wolfe framework with Nesterov acceleration, yielding a projection-free constrained optimization strategy that stabilizes training dynamics. Experiments on six benchmark datasets show that LDC-GAT outperforms GAT by 10.54% in classification accuracy, which demonstrates strong robustness on heterophilic graphs. Full article

(This article belongs to the Section Mathematical Analysis)

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13 pages, 281 KiB

Open AccessArticle

m-Isometric Operators with Null Symbol and Elementary Operator Entries

by Bhagwati Prashad Duggal

Axioms 2025, 14(7), 503; https://doi.org/10.3390/axioms14070503 - 27 Jun 2025

Abstract

A pair

(A, B)

of Banach space operators is strict

(m, X)

-isometric for a Banach space operator

X \in B (X)

and a positive integer m if [...] Read more.

A pair

(A, B)

of Banach space operators is strict

(m, X)

-isometric for a Banach space operator

X \in B (X)

and a positive integer m if

▵_{A, B}^{m} (X) = (\sum_{j = 0}^{m} (\begin{matrix} m \\ j \end{matrix}) L_{A}^{j} R_{B}^{j}) (X) = 0

and

▵_{A, B}^{m - 1} (X) \neq 0

, where

L_{A}

and

R_{B} \in B (B (X))

are, respectively, the operators of left multiplication by A and right multiplication by B. Define operators

E_{A, B}

and

E_{A, B} (X)

by

E_{A, B} = L_{A} R_{B}

and

{(E_{A, B} (X))}^{n} = E_{A, B}^{n} (X)

for all non-negative integers n. Using little more than an algebraic argument, the following generalised version of a result relating

(m, X)

-isometric properties of pairs

(A_{1}, A_{2})

and

(B_{1}, B_{2})

to pairs

(E_{A_{1}, A_{2}} (S_{1}), E_{B_{1}, B_{2}} (S_{2}))

and

(E_{A_{1}, A_{2}}, E_{B_{1}, B_{2}})

is proved: if

A_{i}, B_{i}, S_{i}, X

are operators in

B (X)

,

1 \leq i \leq 2

and X a quasi-affinity, then the pair

(E_{A_{1}, A_{2}} (S_{1}), E_{B_{1}, B_{2}} (S_{2}))

(resp., the pair

(E_{A_{1}, A_{2}}, E_{B_{1}, B_{2}})

) is strict

(m, X)

-isometric for all

X \in B (X)

if and only if there exist positive integers

m_{i} \leq m

,

1 \leq i \leq 2

and

m = m_{1} + m_{2} - 1

, and a non-zero scalar

β

such that

I - E_{β A_{1}, A_{2}} (S_{1})

is (strict)

m_{1}

-nilpotent and

I - E_{\frac{1}{β} B_{1}, B_{2}} (S_{2})

is (strict)

m_{2}

-nilpotent (resp.,

(β A_{1}, B_{1})

is strict

(m_{1}, I)

-isometric and

(\frac{1}{β} B_{2}, A_{2})

is strict

(m_{2}, I)

-isometric). Full article

(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)

22 pages, 327 KiB

Open AccessArticle

Bayesian Analysis of the Doubly Truncated Zubair-Weibull Distribution: Parameter Estimation, Reliability, Hazard Rate and Prediction

by Zakiah I. Kalantan, Mai A. Hegazy, Abeer A. EL-Helbawy, Hebatalla H. Mohammad, Doaa S. A. Soliman, Gannat R. AL-Dayian and Mervat K. Abd Elaal

Axioms 2025, 14(7), 502; https://doi.org/10.3390/axioms14070502 - 26 Jun 2025

Abstract

This paper discusses the Bayesian estimation for the unknown parameters, reliability and hazard rate functions of the doubly truncated Zubair-Weibull distribution. Informative priors (gamma distribution) for the parameters are used to obtain the posterior distributions. Under the squared-error and linear–exponential loss functions, the [...] Read more.

This paper discusses the Bayesian estimation for the unknown parameters, reliability and hazard rate functions of the doubly truncated Zubair-Weibull distribution. Informative priors (gamma distribution) for the parameters are used to obtain the posterior distributions. Under the squared-error and linear–exponential loss functions, the Bayes estimators are derived. Credible intervals for the parameters, reliability and hazard rate functions are obtained. Bayesian prediction (point and interval) for the future observation is considered under the two-sample prediction scheme. A simulation study is performed using the Markov Chain Monte Carlo algorithm of simulation for different sample sizes to assess the performance of the estimators. Two real datasets are applied to show the flexibility and applicability of the distribution. Full article

15 pages, 283 KiB

Open AccessArticle

by Shoshana Abramovich

Axioms 2025, 14(7), 501; https://doi.org/10.3390/axioms14070501 - 26 Jun 2025

Abstract

The focus of this paper is on three types of convexity: generalized uniform convexity,

Φ

-convexity and superquadracity. The similar structures of these types of convexity are such that the same processes can be applied to each one of them to obtain further [...] Read more.

The focus of this paper is on three types of convexity: generalized uniform convexity,

Φ

-convexity and superquadracity. The similar structures of these types of convexity are such that the same processes can be applied to each one of them to obtain further refinements of known inequalities. Full article

(This article belongs to the Special Issue Theory of Functions and Applications, 3rd Edition)

23 pages, 2188 KiB

Open AccessArticle

Statistical Analysis of a Generalized Linear Model for Bilateral Correlated Data Under Donner’s Model

by Jinlong Cheng, Zhiming Li and Keyi Mou

Axioms 2025, 14(7), 500; https://doi.org/10.3390/axioms14070500 - 26 Jun 2025

Abstract

Paired data often arise in medical studies, with a correlation between responses of paired organs or parts. Under an intra-correlated model, this paper proposes a generalized linear model to investigate probable confounding factors of the individual response rates in paired data. The main [...] Read more.

Paired data often arise in medical studies, with a correlation between responses of paired organs or parts. Under an intra-correlated model, this paper proposes a generalized linear model to investigate probable confounding factors of the individual response rates in paired data. The main link functions include logistic, log–log, complementary log–log, probit, and double exponential. The estimators of model parameters are calculated through the Newton–Raphson, quadratic lower bound, and Fisher bounded algorithms. Then, three tests (i.e., likelihood ratio test, Wald-type test, and score test) are constructed to analyze whether covariates significantly affect the response rate. Finally, the proposed methods are illustrated by numerical simulation and visual impairment data from Iran. Full article

(This article belongs to the Special Issue Recent Stochastic and Statistical Approaches for Modeling Complex Systems and Dependent Variables)

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