Research

Open AccessArticle

Aggregate Bound Choices about Random and Nonrandom Goods Studied via a Nonlinear Analysis

by

Fabrizio Maturo

and

Pierpaolo Angelini

Mathematics 2023, 11(11), 2498; https://doi.org/10.3390/math11112498 - 29 May 2023

Cited by 1 | Viewed by 592

Abstract

In this paper, bound choices are made after summarizing a finite number of alternatives. This means that each choice is always the barycenter of masses distributed over a finite set of alternatives. More than two marginal goods at a time are not handled. [...] Read more.

In this paper, bound choices are made after summarizing a finite number of alternatives. This means that each choice is always the barycenter of masses distributed over a finite set of alternatives. More than two marginal goods at a time are not handled. This is because a quadratic metric is used. In our models, two marginal goods give rise to a joint good, so aggregate bound choices are shown. The variability of choice for two marginal goods that are the components of a multiple good is studied. The weak axiom of revealed preference is checked and mean quadratic differences connected with multiple goods are proposed. In this paper, many differences from vast majority of current research about choices and preferences appear. First of all, conditions of certainty are viewed to be as an extreme simplification. In fact, in almost all circumstances, and at all times, we all find ourselves in a state of uncertainty. Secondly, the two notions, probability and utility, on which the correct criterion of decision-making depends, are treated inside linear spaces over

R

having a different dimension in accordance with the pure subjectivistic point of view. Full article

(This article belongs to the Special Issue Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications)

Open AccessArticle

Novel Algorithms with Inertial Techniques for Solving Constrained Convex Minimization Problems and Applications to Image Inpainting

by

Adisak Hanjing

and

Suthep Suantai

Mathematics 2023, 11(8), 1813; https://doi.org/10.3390/math11081813 - 11 Apr 2023

Viewed by 537

Abstract

In this paper, we propose two novel inertial forward–backward splitting methods for solving the constrained convex minimization of the sum of two convex functions,

φ_{1} + φ_{2},

in Hilbert spaces and analyze their convergence behavior under some conditions. For the [...] Read more.

In this paper, we propose two novel inertial forward–backward splitting methods for solving the constrained convex minimization of the sum of two convex functions,

φ_{1} + φ_{2},

in Hilbert spaces and analyze their convergence behavior under some conditions. For the first method (iFBS), we use the forward–backward operator. The step size of this method depends on a constant of the Lipschitz continuity of

\nabla φ_{1},

hence a weak convergence result of the proposed method is established under some conditions based on a fixed point method. With the second method (iFBS-L), we modify the step size of the first method, which is independent of the Lipschitz constant of

\nabla φ_{1}

by using a line search technique introduced by Cruz and Nghia. As an application of these methods, we compare the efficiency of the proposed methods with the inertial three-operator splitting (iTOS) method by using them to solve the constrained image inpainting problem with nuclear norm regularization. Moreover, we apply our methods to solve image restoration problems by using the least absolute shrinkage and selection operator (LASSO) model, and the results are compared with those of the forward–backward splitting method with line search (FBS-L) and the fast iterative shrinkage-thresholding method (FISTA). Full article

(This article belongs to the Special Issue Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications)

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Open AccessArticle

Common Fixed Point Results in Bicomplex Valued Metric Spaces with Application

by

Amer Hassan Albargi

,

Amnah Essa Shammaky

and

Jamshaid Ahmad

Mathematics 2023, 11(5), 1207; https://doi.org/10.3390/math11051207 - 01 Mar 2023

Cited by 2 | Viewed by 584

Abstract

The purpose of this paper is to establish common fixed points of six mappings in the context of bicomplex valued metric spaces. In this way, we generalize some previous well-known results from the literature. Moreover, we provide a non-trivial example to demonstrate the [...] Read more.

The purpose of this paper is to establish common fixed points of six mappings in the context of bicomplex valued metric spaces. In this way, we generalize some previous well-known results from the literature. Moreover, we provide a non-trivial example to demonstrate the authenticity of established outcomes. As an application, we investigate the solution of an Urysohn integral equation by applying our results. Full article

(This article belongs to the Special Issue Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications)

Open AccessArticle

A Convergent Algorithm for Equilibrium Problem to Predict Prospective Mathematics Teachers’ Technology Integrated Competency

by

Nipa Jun-on

,

Watcharaporn Cholamjiak

and

Raweerote Suparatulatorn

Mathematics 2022, 10(23), 4464; https://doi.org/10.3390/math10234464 - 26 Nov 2022

Viewed by 716

Abstract

Educational data classification has become an effective tool for exploring the hidden pattern or relationship in educational data and predicting students’ performance or teachers’ competency. This study proposes a new method based on machine learning algorithms to predict the technology-integrated competency of pre-service [...] Read more.

Educational data classification has become an effective tool for exploring the hidden pattern or relationship in educational data and predicting students’ performance or teachers’ competency. This study proposes a new method based on machine learning algorithms to predict the technology-integrated competency of pre-service mathematics teachers. In this paper, we modified the inertial subgradient extragradient algorithm for pseudomonotone equilibrium and proved the weak convergence theorem under some suitable conditions in Hilbert spaces. We then applied to solve data classification by extreme learning machine using the dataset comprised of the technology-integrated competency of 954 pre-service mathematics teachers in a university in northern Thailand, longitudinally collected for five years. The flexibility of our algorithm was shown by comparisons of the choice of different parameters. The performance was calculated and compared with the existing algorithms to be implemented for prediction. The results show that the proposed method achieved a classification accuracy of 81.06%. The predictions were implemented using ten attributes, including demographic information, skills, and knowledge relating to technology developed throughout the teacher education program. Such data driven studies are significant for establishing a prospective teacher competency analysis framework in teacher education and contributing to decision-making for policy design. Full article

(This article belongs to the Special Issue Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications)

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Open AccessFeature PaperArticle

A Modified Inertial Parallel Viscosity-Type Algorithm for a Finite Family of Nonexpansive Mappings and Its Applications

by

Suthep Suantai

,

Kunrada Kankam

,

Damrongsak Yambangwai

and

Watcharaporn Cholamjiak

Mathematics 2022, 10(23), 4422; https://doi.org/10.3390/math10234422 - 23 Nov 2022

Viewed by 716

Abstract

In this work, we aim to prove the strong convergence of the sequence generated by the modified inertial parallel viscosity-type algorithm for finding a common fixed point of a finite family of nonexpansive mappings under mild conditions in real Hilbert spaces. Moreover, we [...] Read more.

In this work, we aim to prove the strong convergence of the sequence generated by the modified inertial parallel viscosity-type algorithm for finding a common fixed point of a finite family of nonexpansive mappings under mild conditions in real Hilbert spaces. Moreover, we present the numerical experiments to solve linear systems and differential problems using Gauss–Seidel, weight Jacobi, and successive over relaxation methods. Furthermore, we provide our algorithm to show the efficiency and implementation of the LASSO problems in signal recovery. The novelty of our algorithm is that we show that the algorithm is efficient compared with the existing algorithms. Full article

(This article belongs to the Special Issue Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications)

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Open AccessArticle

Existence and Approximation of Fixed Points of Enriched φ-Contractions in Banach Spaces

by

Vasile Berinde

,

Jackie Harjani

and

Kishin Sadarangani

Mathematics 2022, 10(21), 4138; https://doi.org/10.3390/math10214138 - 05 Nov 2022

Viewed by 890

Abstract

We introduce the class of enriched

φ

-contractions in Banach spaces as a natural generalization of

φ

-contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of [...] Read more.

We introduce the class of enriched

φ

-contractions in Banach spaces as a natural generalization of

φ

-contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of mappings in the setting of a Banach space. We illustrated the usefulness of our fixed point results by studying the existence and uniqueness of the solutions of some second order

(p, q)

-difference equations with integral boundary value conditions. Full article

(This article belongs to the Special Issue Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications)

Open AccessArticle

Generalized Hukuhara Weak Solutions for a Class of Coupled Systems of Fuzzy Fractional Order Partial Differential Equations without Lipschitz Conditions

by

Fan Zhang

,

Heng-You Lan

and

Hai-Yang Xu

Mathematics 2022, 10(21), 4033; https://doi.org/10.3390/math10214033 - 30 Oct 2022

Cited by 2 | Viewed by 890

Abstract

As is known to all, Lipschitz condition, which is very important to guarantee existence and uniqueness of solution for differential equations, is not frequently satisfied in real-world problems. In this paper, without the Lipschitz condition, we intend to explore a kind of novel [...] Read more.

As is known to all, Lipschitz condition, which is very important to guarantee existence and uniqueness of solution for differential equations, is not frequently satisfied in real-world problems. In this paper, without the Lipschitz condition, we intend to explore a kind of novel coupled systems of fuzzy Caputo Generalized Hukuhara type (in short, gH-type) fractional partial differential equations. First and foremost, based on a series of notions of relative compactness in fuzzy number spaces, and using Schauder fixed point theorem in Banach semilinear spaces, it is naturally to prove existence of two classes of gH-weak solutions for the coupled systems of fuzzy fractional partial differential equations. We then give an example to illustrate our main conclusions vividly and intuitively. As applications, combining with the relevant definitions of fuzzy projection operators, and under some suitable conditions, existence results of two categories of gH-weak solutions for a class of fire-new fuzzy fractional partial differential coupled projection neural network systems are also proposed, which are different from those already published work. Finally, we present some work for future research. Full article

(This article belongs to the Special Issue Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications)

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Open AccessArticle

Some Congruences for the Coefficients of Rogers–Ramanujan Type Identities

by

Vasudha Gupta

and

Meenakshi Rana

Mathematics 2022, 10(19), 3582; https://doi.org/10.3390/math10193582 - 01 Oct 2022

Viewed by 654

Abstract

We examine a few mathematical characteristics of Rogers–Ramanujan type identities as a follow-up work. Recently authors interpreted Rogers–Ramanujan type identities combinatorially using signed color partitions. In the present study, we discovered several congruences for the coefficients of powers of q that are in [...] Read more.

We examine a few mathematical characteristics of Rogers–Ramanujan type identities as a follow-up work. Recently authors interpreted Rogers–Ramanujan type identities combinatorially using signed color partitions. In the present study, we discovered several congruences for the coefficients of powers of q that are in arithmetic progressions modulo powers of 2 and 3. Full article

(This article belongs to the Special Issue Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications)

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