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Axioms
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Nonlinear Functional Analysis in Natural Sciences
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Nonlinear Functional Analysis in Natural Sciences

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

Deadline for manuscript submissions: closed (20 November 2023) | Viewed by 5597

Special Issue Editors

Prof. Dr. Boško Damjanović

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Guest Editor
Department of Mathematics, University Union—Nikola Tesla, Belgrade, Serbia
Interests: real analysis; integration; mapping; analysis; real and complex analysis; topology; mathematical analysis; functional analysis
Dr. Pradip Debnath

E-Mail Website
Guest Editor
Department of Applied Science and Humanities, Assam University Silchar, Silchar, India
Interests: functional analysis; fixed point theory and fractional calculus; fuzzy mathematics; Geographic Information System; mathematical statistics

Special Issue Information

Dear Colleagues,

The techniques in functional analysis have widespread applications in the modeling of numerous natural phenomena. As such, these techniques and tools are multidisciplinary in nature and indispensable in the study of natural sciences. Fixed-point theory, fractional calculus, partial differential equations, integral equations, wavelet analysis, and approximation theory are some spearhead topics that heavily employ the tools of nonlinear functional analysis. The increased complexity in physical phenomena and engineering experiments continually seeks the advancement of these analytic tools.

This Special Issue provides a unified framework for the study of several problems arising from the modeling of diverse processes in natural sciences. This Special Issue will collect new research findings of the highest quality with novelty and illustrative examples with a sustainable impact on the existing literature that use nonlinear functional analytical tools.

Potential Topics to be Covered: Real and complex functions; functional analysis; fixed points; nonlinear operator theory; variational inequalities; numerical analysis and algorithms; functional equations and stability; partial differential equations; integral equations; calculus of variation; wavelet analysis; fractional calculus; fluid mechanics; and analytic number theory.

Prof. Dr. Boško Damjanović
Dr. Pradip Debnath
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

  • real and complex functions
  • functional analysis
  • fixed points
  • nonlinear operator theory
  • variational inequalities
  • numerical analysis and algorithms
  • functional equations and stability
  • partial differential equations
  • integral equations
  • calculus of variation
  • wavelet analysis
  • fractional calculus
  • fluid mechanics
  • analytic number theory

Published Papers (5 papers)

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Research

17 pages, 555 KiB  
Article
Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point Problems
by Doaa Filali, Mohammad Dilshad, Lujain Saud Muaydhid Alyasi and Mohammad Akram
Axioms 2023, 12(9), 848; https://doi.org/10.3390/axioms12090848 - 30 Aug 2023
Cited by 1 | Viewed by 672
Abstract
This paper aims to present two inertial iterative algorithms for estimating the solution of split variational inclusion (SpVIsP) and its extended version for estimating the common solution of (SpVIsP) and fixed [...] Read more.
This paper aims to present two inertial iterative algorithms for estimating the solution of split variational inclusion (SpVIsP) and its extended version for estimating the common solution of (SpVIsP) and fixed point problem (FPP) of a nonexpansive mapping in the setting of real Hilbert spaces. We establish the weak convergence of the proposed algorithms and strong convergence of the extended version without using the pre-estimated norm of a bounded linear operator. We also exhibit the reliability and behavior of the proposed algorithms using appropriate assumptions in a numerical example. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis in Natural Sciences)
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12 pages, 289 KiB  
Article
Fixed-Point Theorems for Nonlinear Contraction in Fuzzy-Controlled Bipolar Metric Spaces
by Gunaseelan Mani, Arul Joseph Gnanaprakasam, Santosh Kumar, Ozgur Ege and Manuel De la Sen
Axioms 2023, 12(4), 396; https://doi.org/10.3390/axioms12040396 - 19 Apr 2023
Cited by 1 | Viewed by 783
Abstract
In this paper, we introduce the concept of fuzzy-controlled bipolar metric space and prove some fixed-point theorems in this space. Our results generalize and expand some of the literature’s well-known results. We also provide some applications of our main results to integral equations. [...] Read more.
In this paper, we introduce the concept of fuzzy-controlled bipolar metric space and prove some fixed-point theorems in this space. Our results generalize and expand some of the literature’s well-known results. We also provide some applications of our main results to integral equations. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis in Natural Sciences)
17 pages, 364 KiB  
Article
Fixed Point Theorems via Orthogonal Convex Contraction in Orthogonal ♭-Metric Spaces and Applications
by Gunasekaran Nallaselli, Amani S. Baazeem, Arul Joseph Gnanaprakasam, Gunaseelan Mani, Khalil Javed, Eskandar Ameer and Nabil Mlaiki
Axioms 2023, 12(2), 143; https://doi.org/10.3390/axioms12020143 - 30 Jan 2023
Cited by 2 | Viewed by 952
Abstract
In this paper, we introduce the concept of orthogonal convex structure contraction mapping and prove some fixed point theorems on orthogonal ♭-metric spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the [...] Read more.
In this paper, we introduce the concept of orthogonal convex structure contraction mapping and prove some fixed point theorems on orthogonal ♭-metric spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of the solution for the spring-mass system via an integral equation with a numerical example. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis in Natural Sciences)
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10 pages, 273 KiB  
Article
Fixed Point Results for a Family of Interpolative F-Contractions in b-Metric Spaces
by Nabanita Konwar and Pradip Debnath
Axioms 2022, 11(11), 621; https://doi.org/10.3390/axioms11110621 - 07 Nov 2022
Cited by 2 | Viewed by 1048
Abstract
In this paper, we introduce a new generalized concept, namely, extended interpolative Cirić–Reich–Rus-type F-contraction in b-metric space. In addition, we put forward the notion of interpolative Kannan-type F-contractions. Fixed point results for these new interpolative contraction mappings are established, and [...] Read more.
In this paper, we introduce a new generalized concept, namely, extended interpolative Cirić–Reich–Rus-type F-contraction in b-metric space. In addition, we put forward the notion of interpolative Kannan-type F-contractions. Fixed point results for these new interpolative contraction mappings are established, and non-trivial examples involving finite and infinite sets are provided to validate the results. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis in Natural Sciences)
9 pages, 268 KiB  
Article
Approximating Solutions of Optimization Problems via Fixed Point Techniques in Geodesic Spaces
by Rahul Shukla
Axioms 2022, 11(10), 492; https://doi.org/10.3390/axioms11100492 - 22 Sep 2022
Viewed by 1001
Abstract
The principal objective of this paper is to find the solution to a constrained minimization problem and the zero of the monotone operator in geodesic spaces. The basic tool in our study is a nonexpansive mapping. Further, we employ the general Picard–Mann iterative [...] Read more.
The principal objective of this paper is to find the solution to a constrained minimization problem and the zero of the monotone operator in geodesic spaces. The basic tool in our study is a nonexpansive mapping. Further, we employ the general Picard–Mann iterative method to approximate fixed points of nonexpansive mappings under various conditions. We obtain certain theorems concerning Δ and strong convergence. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis in Natural Sciences)
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