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Axioms
Special Issues
Advances in Nonlinear Analysis and Related Fixed Point Problems
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Advances in Nonlinear Analysis and Related Fixed Point Problems

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (31 May 2022) | Viewed by 6961

Special Issue Editors

Prof. Dr. Chiming Chen

E-Mail Website
Guest Editor
Institute for Computational and Modeling Science, National Tsing Hua University, 521 Nan-Dah Road, Hsinchu City 30013, Taiwan
Interests: mathematical analysis; functional analysis; fixed-point theory
Dr. Andreea Fulga

E-Mail Website
Co-Guest Editor
Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov, 500036 Brasov, Romania
Interests: mathematical analysis; operator theory; real analysis; functional analysis
Special Issues, Collections and Topics in MDPI journals
Assist. Prof. Dr. Karpagam Saravanan

E-Mail Website
Co-Guest Editor
Department of Science and Humanities Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602 105, India
Interests: functional analysis; nonlinear analysis; fixed point theory

Special Issue Information

Dear Colleagues,

Nonlinear analysis has wide and significant applications in many areas of mathematics, including functional analysis, variational analysis, nonlinear optimization, convex analysis, nonlinear ordinary and partial differential equations, and so forth. Fixed point theory is a very strong mathematical tool to establish the existence and uniqueness of almost all problems modelled by nonlinear relations. For about a century, fixed point theory has begun to take shape, and developed rapidly. Due to its applications, fixed point theory is highly appreciated and continues to be explored. Besides, fixed point theory can be applied in many types of spaces, such as soft metric spaces, random metric spaces and Sobolev spaces. This feature of fixed-point theory makes is very valuable in studying numerous problems of practical sciences modelled by fractional ordinary and partial differential and difference equations.

In this Special Issue, we will focus on the connection between nonlinear analysis and fixed-point theory as well as their applications to integrate basic science into the real world. We cordially and earnestly invite researchers to contribute their original and high-quality research papers which will inspire advances in nonlinear analysis, fixed point theory, and their applications. Potential topics include but are not limited to:

  • Functional analysis;
  • Fixed point, coincidence point, and best proximity point theory;
  • Critical point theory;
  • KKM theory;
  • Set-valued analysis;
  • Critical point theory;
  • Dynamical systems;
  • Soft theory;
  • Convex analysis;
  • Game theory;
  • Graph theory and optimization;

Prof. Dr. Chiming Chen
Dr. Andreea Fulga
Assist. Prof. Dr. Karpagam Saravanan
Guest Editors

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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • Functional analysis
  • Fixed point, coincidence point, and best proximity point theory
  • Critical point theory
  • KKM theory
  • Set-valued analysis
  • Critical point theory
  • Dynamical systems
  • Soft theory
  • Convex analysis
  • Game theory
  • Graph theory and optimization

Published Papers (4 papers)

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Research

18 pages, 350 KiB  
Article
Solving Fractional Volterra–Fredholm Integro-Differential Equations via A** Iteration Method
by Austine Efut Ofem, Aftab Hussain, Oboyi Joseph, Mfon Okon Udo, Umar Ishtiaq, Hamed Al Sulami and Chukwuka Fernando Chikwe
Axioms 2022, 11(9), 470; https://doi.org/10.3390/axioms11090470 - 14 Sep 2022
Cited by 4 | Viewed by 1482
Abstract
In this article, we develop a faster iteration method, called the A∗∗ iteration method, for approximating the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. We establish some weak and strong convergence results of the A∗∗ [...] Read more.
In this article, we develop a faster iteration method, called the A∗∗ iteration method, for approximating the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. We establish some weak and strong convergence results of the A∗∗ iteration method for fixed points of generalized α-nonexpansive mappings in uniformly convex Banach spaces. We provide a numerical example to illustrate the efficiency of our new iteration method. The weak w2-stability result of the new iteration method is also studied. As an application of our main results, we approximate the solution of a fractional Volterra–Fredholm integro-differential equation. Our results improve and generalize several well-known results in the current literature. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Related Fixed Point Problems)
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9 pages, 269 KiB  
Article
Multiplicity of Positive Solutions to Nonlocal Boundary Value Problems with Strong Singularity
by Chan-Gyun Kim
Axioms 2022, 11(1), 7; https://doi.org/10.3390/axioms11010007 - 23 Dec 2021
Viewed by 1798
Abstract
In this paper, we consider generalized Laplacian problems with nonlocal boundary conditions and a singular weight, which may not be integrable. The existence of two positive solutions to the given problem for parameter λ belonging to some open interval is shown. Our approach [...] Read more.
In this paper, we consider generalized Laplacian problems with nonlocal boundary conditions and a singular weight, which may not be integrable. The existence of two positive solutions to the given problem for parameter λ belonging to some open interval is shown. Our approach is based on the fixed point index theory. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Related Fixed Point Problems)
5 pages, 229 KiB  
Article
Fixed Point Results for Frum-Ketkov Type Contractions in b-Metric Spaces
by Cristian Chifu, Erdal Karapınar and Gabriela Petrusel
Axioms 2021, 10(3), 231; https://doi.org/10.3390/axioms10030231 - 18 Sep 2021
Cited by 2 | Viewed by 1166
Abstract
The purpose of this paper is to present some fixed point results for Frum-Ketkov type operators in complete b-metric spaces. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Related Fixed Point Problems)
13 pages, 306 KiB  
Article
θ*-Weak Contractions and Discontinuity at the Fixed Point with Applications to Matrix and Integral Equations
by Atiya Perveen, Waleed M. Alfaqih, Salvatore Sessa and Mohammad Imdad
Axioms 2021, 10(3), 209; https://doi.org/10.3390/axioms10030209 - 31 Aug 2021
Cited by 2 | Viewed by 1547
Abstract
In this paper, the notion of θ*-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan and Rhoades on the existence of [...] Read more.
In this paper, the notion of θ*-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan and Rhoades on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Related Fixed Point Problems)
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