New Trends in Nonlinear Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 8590

Special Issue Editor


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Guest Editor
Department of Mathematics, Guru Ghasidas Vishwavidyalaya (A Central University), Bilaspur 495009, India
Interests: nonlinear analysis; fixed point theory; fuzzy mathematics

Special Issue Information

Dear Colleagues,

Nonlinear analysis is an area of mathematics which is influenced by nonlinear problems occurring in physics, biology, computer science, mechanics, economics etc. Its scope is much wider than that of linear system analysis, as most problems arising in the natural or social sciences are not necessarily linear.

This Special Issue is focused on the latest developments in nonlinear analysis and its applications. Nonlinear analysis falls within the general area of nonlinear functional analysis—an area which has been of increasing research interest in recent years. Nonlinear analytical theory applies to diverse nonlinear problems in many areas, such as differential equations, nonlinear ergodic theory, optimization problems, control theory, variational inequality problems, equilibrium problems, and split feasibility problems.

This Special Issue will reflect both the state-of-the-art theoretical research and important recent advances in applications. We are interested in high-quality articles that outline recent progress in this area of research. In addition to the topics listed below, high-quality articles on new concepts, methods, algorithms, and applications to various branches of science will equally be entertained.

Potential topics include but are not limited to the following:

  • Nonlinear ergodic theory and applications;
  • Solutions to differential equations and control theory problems;
  • Dynamical systems and bifurcation;
  • Mathematical modelling dealing nonlinear phenomena;
  • Optimization problems, equilibrium problems,
  • Split feasibility problems, and applications;
  • Implications of fixed-point theory to non-linear problems;
  • Convergence and stability of iterative algorithms.

Dr. Dhananjay Gopal
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.

Published Papers (8 papers)

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Research

14 pages, 434 KiB  
Article
A New Adaptive Eleventh-Order Memory Algorithm for Solving Nonlinear Equations
by Sunil Panday, Shubham Kumar Mittal, Carmen Elena Stoenoiu and Lorentz Jäntschi
Mathematics 2024, 12(12), 1809; https://doi.org/10.3390/math12121809 - 11 Jun 2024
Viewed by 287
Abstract
In this article, we introduce a novel three-step iterative algorithm with memory for finding the roots of nonlinear equations. The convergence order of an established eighth-order iterative method is elevated by transforming it into a with-memory variant. The improvement in the convergence order [...] Read more.
In this article, we introduce a novel three-step iterative algorithm with memory for finding the roots of nonlinear equations. The convergence order of an established eighth-order iterative method is elevated by transforming it into a with-memory variant. The improvement in the convergence order is achieved by introducing two self-accelerating parameters, calculated using the Hermite interpolating polynomial. As a result, the R-order of convergence for the proposed bi-parametric with-memory iterative algorithm is enhanced from 8 to 10.5208. Notably, this enhancement in the convergence order is accomplished without the need for extra function evaluations. Moreover, the efficiency index of the newly proposed with-memory iterative algorithm improves from 1.5157 to 1.6011. Extensive numerical testing across various problems confirms the usefulness and superior performance of the presented algorithm relative to some well-known existing algorithms. Full article
(This article belongs to the Special Issue New Trends in Nonlinear Analysis)
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11 pages, 1181 KiB  
Article
Passive Stabilization of Static Output Feedback of Disturbed Nonlinear Stochastic System
by Ping-Tzan Huang, Chein-Chung Sun, Cheung-Chieh Ku and Yun-Chen Yeh
Mathematics 2023, 11(21), 4435; https://doi.org/10.3390/math11214435 - 26 Oct 2023
Viewed by 652
Abstract
This paper investigates the Static Output (SO) control issue of the disturbed nonlinear stochastic system, which achieves passivity. Through the application of fuzzy sets and the stochastic differential equation, a Takagi–Sugeno (T-S) fuzzy model with the terms of multiplicative noise and external disturbance [...] Read more.
This paper investigates the Static Output (SO) control issue of the disturbed nonlinear stochastic system, which achieves passivity. Through the application of fuzzy sets and the stochastic differential equation, a Takagi–Sugeno (T-S) fuzzy model with the terms of multiplicative noise and external disturbance can be constructed to describe the considered systems. Furthermore, the Parallel Distributed Compensation (PDC) concept is used to design a fuzzy controller exhibiting an SO feedback scheme structure. To attenuate the effect of external disturbance, the PDC-based SO fuzzy controller is designed to exhibit passivity. During the derivation of some sufficient conditions, a line-integral Lyapunov function is utilized to avoid the conservative term produced using the derivative membership function. Using converting technologies, a stability criterion belonging to Linear Matrix Inequality (LMI) forms is proposed such that the derived conditions are convex hull problems and are solved through an optimization algorithm. Then, the proposed criterion is used to discuss the problem of SO controller design of ship fin stabilizing systems with added disturbance and noise. Full article
(This article belongs to the Special Issue New Trends in Nonlinear Analysis)
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12 pages, 256 KiB  
Article
On an Extension of a Spare Regularization Model
by Abdellatif Moudafi
Mathematics 2023, 11(20), 4285; https://doi.org/10.3390/math11204285 - 14 Oct 2023
Viewed by 735
Abstract
In this paper, we would first like to promote an interesting idea for identifying the local minimizer of a non-convex optimization problem with the global minimizer of a convex optimization one. Secondly, to give an extension of their sparse regularization model for inverting [...] Read more.
In this paper, we would first like to promote an interesting idea for identifying the local minimizer of a non-convex optimization problem with the global minimizer of a convex optimization one. Secondly, to give an extension of their sparse regularization model for inverting incomplete Fourier transforms introduced. Thirdly, following the same lines, to develop convergence guaranteed efficient iteration algorithm for solving the resulting nonsmooth and nonconvex optimization problem but here using applied nonlinear analysis tools. These both lead to a simplification of the proofs and to make a connection with classical works in this filed through a startling comment. Full article
(This article belongs to the Special Issue New Trends in Nonlinear Analysis)
11 pages, 300 KiB  
Article
Existence and Uniqueness of Positive Solutions for the Fractional Differential Equation Involving the ρ(τ)-Laplacian Operator and Nonlocal Integral Condition
by Piyachat Borisut and Supak Phiangsungnoen
Mathematics 2023, 11(16), 3525; https://doi.org/10.3390/math11163525 - 15 Aug 2023
Cited by 1 | Viewed by 884
Abstract
This paper aims to investigate the Caputo fractional differential equation involving the ρ(τ) Laplacian operator and nonlocal multi-point of Riemann–Liouville’s fractional integral. We also prove the uniqueness of the positive solutions for Boyd and Wong’s nonlinear contraction via the Guo–Krasnoselskii [...] Read more.
This paper aims to investigate the Caputo fractional differential equation involving the ρ(τ) Laplacian operator and nonlocal multi-point of Riemann–Liouville’s fractional integral. We also prove the uniqueness of the positive solutions for Boyd and Wong’s nonlinear contraction via the Guo–Krasnoselskii fixed-point theorem in Banach spaces. Finally, we illustrate the theoretical results and show that by solving the nonlocal problems, it is possible to obtain accurate approximations of the solutions. An example is also provided to illustrate the applications of our theorem. Full article
(This article belongs to the Special Issue New Trends in Nonlinear Analysis)
11 pages, 301 KiB  
Article
Fixed Point Results in Soft Fuzzy Metric Spaces
by Sonam, Ramakant Bhardwaj and Satyendra Narayan
Mathematics 2023, 11(14), 3189; https://doi.org/10.3390/math11143189 - 20 Jul 2023
Cited by 5 | Viewed by 1356
Abstract
The primary objective of the paper is to present the Banach contraction theorem in soft fuzzy metric spaces while taking into consideration a restriction on the soft fuzzy metric between the soft points of the absolute soft set. A new altering distance function, [...] Read more.
The primary objective of the paper is to present the Banach contraction theorem in soft fuzzy metric spaces while taking into consideration a restriction on the soft fuzzy metric between the soft points of the absolute soft set. A new altering distance function, namely the Ψ-contraction function, is introduced on soft fuzzy metric spaces, and some fixed point results are proven by considering soft mappings that comprise Ψ-contraction with the continuity of soft t-norm. In addition to that, some illustrations are supplied for the support of the established soft fuzzy Banach contraction theorem and fixed point results over Ψ-contraction mappings. The obtained results generalize and extend some well-known results present in the literature on fixed point theory. Full article
(This article belongs to the Special Issue New Trends in Nonlinear Analysis)
16 pages, 10116 KiB  
Article
An Inertial Forward–Backward Splitting Method for Solving Modified Variational Inclusion Problems and Its Application
by Kamonrat Sombut, Kanokwan Sitthithakerngkiet, Areerat Arunchai and Thidaporn Seangwattana
Mathematics 2023, 11(9), 2107; https://doi.org/10.3390/math11092107 - 28 Apr 2023
Cited by 1 | Viewed by 971
Abstract
In this paper, we propose an inertial forward–backward splitting method for solving the modified variational inclusion problem. The concept of the proposed method is based on Cholamjiak’s method. and Khuangsatung and Kangtunyakarn’s method. Cholamjiak’s inertial technique is utilized in the proposed method for [...] Read more.
In this paper, we propose an inertial forward–backward splitting method for solving the modified variational inclusion problem. The concept of the proposed method is based on Cholamjiak’s method. and Khuangsatung and Kangtunyakarn’s method. Cholamjiak’s inertial technique is utilized in the proposed method for increased acceleration. Moreover, we demonstrate that the proposed method strongly converges under appropriate conditions and apply the proposed method to solve the image restoration problem where the images have been subjected to various obscuring processes. In our example, we use the proposed method and Khuangsatung and Kangtunyakarn’s method to restore two medical images. To compare image quality, we also evaluate the signal-to-noise ratio (SNR) of the proposed method to that of Khuangsatung and Kangtunyakarn’s method. Full article
(This article belongs to the Special Issue New Trends in Nonlinear Analysis)
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6 pages, 265 KiB  
Article
Remark on a Fixed-Point Theorem in the Lebesgue Spaces of Variable Integrability Lp(·)
by Mohamed A. Khamsi and Osvaldo D. Méndez
Mathematics 2023, 11(1), 157; https://doi.org/10.3390/math11010157 - 28 Dec 2022
Viewed by 913
Abstract
In a personal communication, Prof. Domínguez Benavides noted that a fixed-point theorem for modular nonexpansive mappings in Lp(·)(Ω) obtained under the assumptions p+< and the property (R) satisfied by ρ will [...] Read more.
In a personal communication, Prof. Domínguez Benavides noted that a fixed-point theorem for modular nonexpansive mappings in Lp(·)(Ω) obtained under the assumptions p+< and the property (R) satisfied by ρ will force p>1. Therefore, the conclusion is well known. In this note, we establish said conclusion without the assumption p+<. Full article
(This article belongs to the Special Issue New Trends in Nonlinear Analysis)
20 pages, 508 KiB  
Article
Approximating Common Fixed Points of Nonexpansive Mappings on Hadamard Manifolds with Applications
by Konrawut Khammahawong, Parin Chaipunya and Kamonrat Sombut
Mathematics 2022, 10(21), 4080; https://doi.org/10.3390/math10214080 - 2 Nov 2022
Viewed by 1139
Abstract
The point of this research is to present a new iterative procedure for approximating common fixed points of nonexpansive mappings in Hadamard manifolds. The convergence theorem of the proposed method is discussed under certain conditions. For the sake of clarity, we provide some [...] Read more.
The point of this research is to present a new iterative procedure for approximating common fixed points of nonexpansive mappings in Hadamard manifolds. The convergence theorem of the proposed method is discussed under certain conditions. For the sake of clarity, we provide some numerical examples to support our results. Furthermore, we apply the suggested approach to solve inclusion problems and convex feasibility problems. Full article
(This article belongs to the Special Issue New Trends in Nonlinear Analysis)
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