762 Results Found

In this paper, we give sufficient conditions to ensure the existence of the best proximity point of monotone relatively nonexpansive mappings defined on partially ordered Banach spaces. An example is given to illustrate our results.

Using the deep result of Ran & Reunrings, we generalize existing results for tripled fixed points. In contrast to the previously known results for tripled fixed points of maps with or without the mixed monotone property in partially ordered compl...

We investigate the oscillation of the fourth-order differential equation for a class of functional differential equations of the neutral type. We obtain a new single-oscillation criterion for the oscillation of all the solutions of our equation. We e...

The aim of this work is to provide an iterative process for generating new monotonic properties for positive solutions of the second-order delay differential equation $y^{″}\left(t\right)+p\left(t\right)y\left(\tau \left(t\right)\right)=0$, which will lead to the improvement of known oscillat...

Fractional-order differential operators accentuate weak edges and fine texture more effectively than their integer-order counterparts, but in image enhancement the fractional machinery is confined almost entirely to the spatial stage, while the tonal...

The monotonic properties of positive solutions to functional differential equations of the third order are examined in this paper. It is generally known that by optimizing the relationships between a solution and its corresponding function, as well a...

The quadratic Lyapunov inequality of Aguila-Camacho, Duarte-Mermoud and Gallegos has been extended operator by operator—most recently to the generalised Hattaf mixed operator, which subsumes the Atangana–Baleanu, Hadamard, generalised pro...

We present new results in interval analysis (IA) and in the calculus for interval-valued functions of a single real variable. Starting with a recently proposed comparison index, we develop a new general setting for partial order in the (semi linear)...

In this paper, the issue of robust sensor fault estimation for Takagi–Sugeno (T–S) fuzzy systems with Caputo–Hadamard fractional-order dynamics subject to monotone nonlinearities is addressed. An adaptive observer is designed for th...

This study investigates a symmetric fractional-order epidemic model with time delays and non-monotonic incidence rates, considering two viral strains. By confirming the existence, uniqueness, and boundedness of the system’s solutions, the resea...

The aim of this paper is twofold: introducing the concept of monotone enriched nonexpansive mappings and a faster iterative process. Our examples illustrate the novelty of our newly introduced concepts. We investigate the iterative estimation of fixe...

Iterative algorithms have been utilized for the computation of approximate solutions of stationary and evolutionary problems associated with differential equations. The aim of this article is to introduce concepts of monotone Reich and Chatterjea non...

In this article, we investigate some qualitative properties of solutions to a class of functional differential equations with multi-delay. Using a modified approach, we first derive a number of optimized relations and inequalities that relate the sol...

We unify a known technique used for fixed points and coupled, tripled and N-tupled fixed points for weak monotone maps, i.e., maps that exhibit monotone properties for each of their variables. We weaken the classical contractive condition in partiall...

We establish a Perron–Frobenius-type theorem for the subdominant eigenvalue of Möbius monotone transition matrices defined on partially ordered state spaces. This result extends the classical work of Keilson and Kester, where they consider...

Polypharmacology in Amyotrophic lateral sclerosis (ALS) demands models that capture irreducible higher-order drug co-action. We introduce a categorical–topological pipeline that encodes regimens as truncated multicomplexes with a hypergraph&nda...

This study investigated the scalability of a cognitive multiple-choice test through the Mokken package in the R programming language for statistical computing. A 2019 mathematics West African Examinations Council (WAEC) instrument was used to gather...

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operator...

Currently, two-level Mokken scale analysis for clustered test data is being developed. This paper contributes to this development by providing model-fit procedures for two-level Mokken scale analysis. New theoretical insights suggested that the exist...

In this paper, we first revisit and bring together as a sort of survey, properties of Bernstein polynomials of one variable. Secondly, we extend the results from one variable to several ones, namely—uniform convergence, uniform convergence of t...

Given a monotone ordered multi-dimensional real array A and a real value k, an important question in computation is to establish if k is a member of A by sequentially searching A by comparing k with some of its entries. This search problem and its kn...

In the paper, the authors introduce a unified generalization of the Catalan numbers, the Fuss numbers, the Fuss–Catalan numbers, and the Catalan–Qi function, and discover some properties of the unified generalization, including a product-...

In this paper, we establish a fixed-point theorem for mixed monotone operators in ordered Banach algebras by introducing a novel contraction condition formulated in terms of the product law, which represents a significant departure from the tradition...

The article’s primary focus is on the study of the number of countable non-isomorphic models of linearly ordered theories. The orthogonality of 1-types and their convex closures is employed to analyse a class of theories with a specific type of...

In this article, we present new criteria for testing the oscillation of solutions of higher-order neutral delay differential equation. By deriving new monotonic properties of a class of the positive solutions of the studied equation, we establish bet...

Artificial spin ice provides a versatile platform for investigating geometrical frustration and emergent collective phenomena. However, direct visualization and manipulation of individual magnetic moments remain challenging in conventional nanoscale...

This work aims to derive new inequalities that improve the asymptotic and oscillatory properties of solutions to fourth-order neutral differential equations. The relationships between the solution and its corresponding function play an important role...

A framework of distributed interval observers is introduced for fractional-order multiagent systems in the presence of nonlinearity. First, a frame was designed to construct the upper and lower bounds of the system state. By using monotone system the...

This paper deals with the research of solutions of bounded variation (BV) to evolution inclusion coupled with a time and state dependent maximal monotone operator. Different problems are studied: existence of solutions, unicity of the solution, exist...

We study positive–negative guarded systems of language equations over a fixed finite alphabet. The ambient space is the complete ultrametric space of all formal languages equipped with a length-based distance, where two languages are close when...

Nonadditivity of a fuzzy measure, as an indicator of defectiveness, makes a fuzzy mea-sure less useful in applications compared to additive, probabilistic measures. In order to neutralize this indicator of defectiveness to some degree, it is importan...

This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov’s pseudo distance. In a first p...

New sufficient criteria are obtained for the oscillation of a non-autonomous first order differential equation with non-monotone delays. Both recursive and lower-upper limit types criteria are given. The obtained results improve most recent published...

This paper concerns cascaded, shifted, fractional-order, lead compensators made by the serial connection of two stages introducing their respective phase leads in shifted adjacent frequency ranges. Adding up leads in these intervals gives a flat phas...

In this work, new criteria were established for testing the oscillatory behavior of solutions of a class of even-order delay differential equations. We follow an approach that depends on obtaining new monotonic properties for the decreasing positive...

The oscillation of a first-order differential equation with several non-monotone delays is proposed. We extend the works of Kwong (1991) and Sficas and Stavroulakis (2003) for equations with several delays. Our results not only essentially improve bu...

This paper investigates the local and global character of the unique positive equilibrium of a mixed monotone fractional second-order difference equation with quadratic terms. The corresponding associated map of the equation decreases in the first va...

This study aims to investigate the oscillatory behavior of the solutions of an even-order delay differential equation with distributed deviating arguments. We first study the monotonic properties of positive decreasing solutions or the so-called Knes...

This paper deals with the existence of $\omega$-periodic solutions for nth-order ordinary differential equation involving fixed delay in Banach space E. $L_{n}u\left(t\right)=f(t,u\left(t\right),u(t-\tau )),t\in \mathbb{R},$ where $L_{n}u\left(t\right):=u^{\left(n\right)}\left(t\right)+{\displaystyle \sum _{i=0}^{n-1}}{a}_i{u}^{\left(i\right)}\left(t\right)$, $a_i\in \mathbb{R}$, $i=0,1,\cdots ,n-1$, are constants, $f$...

In the present article, we iteratively deduce new monotonic properties of a class from the positive solutions of fourth-order delay differential equations. We discuss the non-canonical case in which there are possible decreasing positive solutions. T...

We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at $-\infty$, and uniform hyperbolic bounds are derived. The same questions are addressed for the classical Le Roy functi...

In this paper, we study oscillation and asymptotic properties for half-linear second order differential equations with mixed argument of the form ${\left(r\left(t\right){\left(y^{\prime }\left(t\right)\right)}^{\alpha }\right)}^{\prime }=p\left(t\right)y^{\alpha }\left(\tau \left(t\right)\right).$ Such differential equation may possesses two types of nonoscillatory solutio...

In this work, by considering a third-order differential equation with delay-neutral arguments, we investigate the oscillatory behavior of solutions. It is known that the relationships between the solution and its derivatives of different orders, as w...

In this survey, we review some old and new results initiated with the study of expansive mappings. From a variational perspective, we study the convergence analysis of expansive and almost-expansive curves and sequences governed by an evolution equat...

We consider the problem of quantifying the information shared by a pair of random variables $X_1,X_2$ about another variable S. We propose a new measure of shared information, called extractable shared information, that is left monotonic;...

In this paper, we study the solvability of various two-point boundary value problems for $x^{\left(4\right)}=f(t,x,x^{\prime },x^{″},x^{‴}),t\in (0,1),$ where f may be defined and continuous on a suitable bounded...

Recently, the uncertainty aspects of record values have been increasingly studied in the literature. In this paper, we study the residual Tsallis entropy of upper record values coming from random samples. In the continuous case, we define the Tsallis...

The problem of constructing information measures with a well-defined interpretation is of fundamental significance in information theory. A good definition of an information measure entails certain desirable properties while also providing answers to...

We establish adequate conditions for the existence and uniqueness of solutions to systems of two matrix equations when the unknown matrices are raised to a power $k\in [-1,1]\setminus \left\{0\right\}$. The findings from coupled fixed points for ordered pairs...

In this manuscript, we defined (α, F)-contractions in the context of double-controlled metric spaces and partially ordered double-controlled metric spaces. We established new fixed-point results and defined the notion of double-controlled metri...