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Research Trends and Challenges in the Theory of Nonlinear Analysis...
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Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".

Deadline for manuscript submissions: closed (31 March 2024) | Viewed by 17414

Special Issue Editor

Dr. Sumit Chandok

E-Mail Website
Guest Editor
School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147004, India
Interests: nonlinear analysis; variational inequality problem; approximation theory; fixed point theory

Special Issue Information

Dear Colleagues,

Due to its critical applications in numerous fields of science and engineering, such as fixed-point theory, best approximation, stability of functional equations, variational inequality problems, partial differential equations, geometric analysis, quantum calculus, computer-aided geometric design, artificial neural networks, image processing, and problems arising in evolution, Approximation theory is one of the most active research areas in the theory of nonlinear analysis. Furthermore, approximation results involving constructive procedures can be used to solve real-world problems.

The primary goal of this Special Issue, entitled “Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications”, is to provide a platform for researchers and academicians to report on new initiatives and developments in nonlinear analysis and applications. Original research as well as review articles are encouraged.

Potential topics include but are not limited to the following:

  • Nonlinear operator theory and applications;
  • Nonlinear analysis in fractional calculus;
  • New iteration procedures for approximation of fixed points;
  • Optimization problems and applications;
  • Variational inequality problems and their applications;
  • Best proximity point theorems and their applications;
  • Quantum calculus in approximation theory;
  • Integral inclusion problems and their solutions;
  • Multifunction systems and their solutions;
  • New abstract metrics spaces and their topological properties;
  • Stability of functional equations;
  • Topological approaches in nonlinear problems;
  • Multivalued problems;
  • Artificial neural networks and image processing problems.

Dr. Sumit Chandok
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • best approximation
  • optimization problems
  • stability of functional equations
  • variational inequality problems
  • fixed-point problems
  • iterative algorithms
  • image processing algorithms
  • artificial intelligence algorithms
  • fractional calculus

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Published Papers (11 papers)

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Research

10 pages, 270 KiB  
Article
Relation-Theoretic Nonlinear Almost Contractions with an Application to Boundary Value Problems
by Salma Aljawi and Izhar Uddin
Mathematics 2024, 12(9), 1275; https://doi.org/10.3390/math12091275 - 23 Apr 2024
Cited by 4 | Viewed by 909
Abstract
This article investigates certain fixed-point results enjoying nonlinear almost contraction conditions in the setup of relational metric space. Some examples are constructed in order to indicate the profitability of our results. As a practical use of our findings, we demonstrate the existence of [...] Read more.
This article investigates certain fixed-point results enjoying nonlinear almost contraction conditions in the setup of relational metric space. Some examples are constructed in order to indicate the profitability of our results. As a practical use of our findings, we demonstrate the existence of a unique solution to a specific first-order boundary value problem. Full article
(This article belongs to the Special Issue Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications)
16 pages, 1517 KiB  
Article
Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem
by Ahmed Alamer and Mohammad Dilshad
Mathematics 2024, 12(5), 747; https://doi.org/10.3390/math12050747 - 1 Mar 2024
Cited by 1 | Viewed by 1260
Abstract
In this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems (SpCNPP) in such a way that the Halpern iteration and inertial extrapolation are computed simultaneously [...] Read more.
In this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems (SpCNPP) in such a way that the Halpern iteration and inertial extrapolation are computed simultaneously in the beginning of each iteration. We prove the strong convergence of sequences driven by the suggested methods without estimating the norm of bounded linear operator when certain appropriate assumptions are made. We demonstrate the efficiency of our iterative methods and compare them with some related and well-known results using relevant numerical examples. 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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18 pages, 380 KiB  
Article
A Modified Viscosity-Type Self-Adaptive Iterative Algorithm for Common Solution of Split Problems with Multiple Output Sets in Hilbert Spaces
by Mohd Asad, Mohammad Dilshad, Doaa Filali and Mohammad Akram
Mathematics 2023, 11(19), 4175; https://doi.org/10.3390/math11194175 - 5 Oct 2023
Cited by 1 | Viewed by 1186
Abstract
A modified viscosity-type self-adaptive iterative algorithm is presented in this study, having a strong convergence theorem for estimating the common solution to the split generalized equilibrium problem along with the split common null point problem with multiple output sets, subject to some reasonable [...] Read more.
A modified viscosity-type self-adaptive iterative algorithm is presented in this study, having a strong convergence theorem for estimating the common solution to the split generalized equilibrium problem along with the split common null point problem with multiple output sets, subject to some reasonable control sequence restrictions. The suggested algorithm and its immediate consequences are also discussed. The effectiveness of the proposed algorithm is finally demonstrated through analytical examples. The findings presented in this paper will help to consolidate, extend, and improve upon a number of recent findings in the literature. 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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30 pages, 397 KiB  
Article
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 5 | Viewed by 1261
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)
18 pages, 3578 KiB  
Article
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 1292
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, φ1+φ2, 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, φ1+φ2, 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 ∇φ1, 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 ∇φ1 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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20 pages, 301 KiB  
Article
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 - 1 Mar 2023
Cited by 3 | Viewed by 1541
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)
16 pages, 365 KiB  
Article
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 1510
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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21 pages, 3158 KiB  
Article
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 1530
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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16 pages, 338 KiB  
Article
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 - 5 Nov 2022
Cited by 3 | Viewed by 1947
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)
21 pages, 795 KiB  
Article
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 1722
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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23 pages, 331 KiB  
Article
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 - 1 Oct 2022
Viewed by 1520
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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