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Symmetry
Special Issues
Fixed Point Theory and Its Applications Dedicated to the Memory...
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Special Issue "Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 September 2023 | Viewed by 3127

Special Issue Editor

Dr. Alexander Zaslavski

E-Mail Website
Guest Editor
Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel
Interests: variational and optimal control problems on unbounded domains; optimization theory and related topics; infinite products of operators and their applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue on fixed point theory and its applications is dedicated to the memory of  Professor William Arthur Kirk, who passed away on October 20, 2022.

Professor Kirk received his Bachelor’s degree from DePauw University in 1958 and his Ph.D. from the University of Missouri in 1962. From 1962 to 1967, he was an Assistant Professor at the University of California at Riverside. In 1967, he began to work as an Associate Professor at the University of Iowa, where he became a full professor in 1970.

Professor Kirk was an outstanding and internationally famous mathematician who made significant contributions to Nonlinear Functional Analysis, especially fixed-point theory.  He is one of the founders of the modern theory of metric fixed-points, and his works deeply influenced the development of the field. He is known for Kirk’s Fixed-Point Theorem of 1964/1965 and for the Caristi-Kirk Fixed-Point Theorem of 1976.  His achievements and leadership in the field were recognized by the title of Doctor Honoris Causa in 2004 from Maria Curie-Sklodowska University, Poland. Professor Kirk  published three books and 177 journal articles. His book Topics in Metric Fixed Point Theory, written jointly with K. Goebel and published by Cambridge University Press in 1990, is now a classic in the area of fixed-point theory. Professor Kirk was the advisor of thirteen PhD students. 

This Special Issue aims to seek out high-quality articles from researchers in the fixed point theory and other areas of nonlinear functional analysis close to the research activities of Professor Kirk.

Dr. Alexander Zaslavski
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. Symmetry 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

  • symmetry analysis
  • symmetry/asymmetry phenomena
  • symmetry nonlinear system
  • complete metric space
  • contractive mapping
  • symmetry and fixed point
  • iterate
  • nonexpansive mapping
  • set-valued mapping

Published Papers (5 papers)

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Article
Three Convergence Results for Iterates of Nonlinear Mappings in Metric Spaces with Graphs
by
Alexander J. Zaslavski
Symmetry 2023, 15(9), 1756; https://doi.org/10.3390/sym15091756 - 13 Sep 2023
Viewed by 230
Abstract
In 2007, in our joint work with D. Butnariu and S. Reich, we proved that if for a self-mapping of a complete metric that is uniformly continuous on bounded sets all its iterates converge uniformly on bounded sets, then this convergence is stable [...] Read more.
In 2007, in our joint work with D. Butnariu and S. Reich, we proved that if for a self-mapping of a complete metric that is uniformly continuous on bounded sets all its iterates converge uniformly on bounded sets, then this convergence is stable under the presence of small errors. In the present paper, we obtain an extension of this result for self-mappings of a metric space with a graph. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk)
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Article
Recent Advancements in KRH-Interpolative-Type Contractions
by
Ansar Abbas
,
Amjad Ali
,
Hamed Al Sulami
and
Aftab Hussain
Symmetry 2023, 15(8), 1515; https://doi.org/10.3390/sym15081515 - 01 Aug 2023
Viewed by 753
Abstract
The focus of this paper is to conduct a comprehensive analysis of the advancements made in the understanding of Interpolative contraction, building upon the ideas initially introduced by Karapinar in 2018. In this paper, we develop the notion of Interpolative contraction mappings to [...] Read more.
The focus of this paper is to conduct a comprehensive analysis of the advancements made in the understanding of Interpolative contraction, building upon the ideas initially introduced by Karapinar in 2018. In this paper, we develop the notion of Interpolative contraction mappings to the case of non-linear Kannan Interpolative, Riech Rus Ćirić interpolative and Hardy–Roger Interpolative contraction mappings based on controlled function, and prove some fixed point results in the context of controlled metric space, thereby enhancing the current understanding of this particular analysis. Furthermore, we provide a concrete example that illustrates the underlying drive for the investigations presented in this context. An application of the proposed non-linear Interpolative-contractions to the Liouville–Caputo fractional derivatives and fractional differential equations is provided in this paper. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk)
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Article
Hybrid Functions Approach via Nonlinear Integral Equations with Symmetric and Nonsymmetrical Kernel in Two Dimensions
by
Sahar M. Abusalim
,
Mohamed A. Abdou
,
Mohamed A. Abdel-Aty
and
Mohamed E. Nasr
Symmetry 2023, 15(7), 1408; https://doi.org/10.3390/sym15071408 - 13 Jul 2023
Viewed by 399
Abstract
The second kind of two-dimensional nonlinear integral equation (NIE) with symmetric and nonsymmetrical kernel is solved in the Banach space L2[0,1]×L2[0,1]. Here, the NIE’s existence and singular solution [...] Read more.
The second kind of two-dimensional nonlinear integral equation (NIE) with symmetric and nonsymmetrical kernel is solved in the Banach space L2[0,1]×L2[0,1]. Here, the NIE’s existence and singular solution are described in this passage. Additionally, we use a numerical strategy that uses hybrid and block-pulse functions to obtain the approximate solution of the NIE in a two-dimensional problem. For this aim, the two-dimensional NIE will be reduced to a system of nonlinear algebraic equations (SNAEs). Then, the SNAEs can be solved numerically. This study focuses on showing the convergence analysis for the numerical approach and generating an estimate of the error. Examples are presented to prove the efficiency of the approach. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk)
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Article
Banach Fixed Point Theorems in Generalized Metric Space Endowed with the Hadamard Product
by
Saleh Omran
,
Ibtisam Masmali
and
Ghaliah Alhamzi
Symmetry 2023, 15(7), 1325; https://doi.org/10.3390/sym15071325 - 28 Jun 2023
Viewed by 608
Abstract
In this paper, we prove some Banach fixed point theorems in generalized metric space where the contractive conditions are endowed with the Hadamard product of real symmetric positive definite matrices. Since the condition that a matrix A converges to zero is not needed, [...] Read more.
In this paper, we prove some Banach fixed point theorems in generalized metric space where the contractive conditions are endowed with the Hadamard product of real symmetric positive definite matrices. Since the condition that a matrix A converges to zero is not needed, this produces stronger results than those of Perov. As an application of our results, we study the existence and uniqueness of the solution for a system of matrix equations. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk)
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Article
Computational Techniques for Solving Mixed (1 + 1) Dimensional Integral Equations with Strongly Symmetric Singular Kernel
by
Sharifah E. Alhazmi
,
Amr M. S. Mahdy
,
Mohamed A. Abdou
and
Doaa Sh. Mohamed
Symmetry 2023, 15(6), 1284; https://doi.org/10.3390/sym15061284 - 19 Jun 2023
Cited by 2 | Viewed by 599
Abstract
This paper describes an effective strategy based on Lerch polynomial method for solving mixed integral equations (MIE) in position and time with a strongly symmetric singular kernel in the space [...] Read more.
This paper describes an effective strategy based on Lerch polynomial method for solving mixed integral equations (MIE) in position and time with a strongly symmetric singular kernel in the space L2(−1,1)×C[0,T],(T<1). The Quadratic numerical method (QNM) was applied to obtain a system of Fredholm integral equations (SFIE), then the Lerch polynomials method (LPM) was applied to transform SFIE into a system of linear algebraic equations (SLAE). The existence and uniqueness of the integral equation’s solution are discussed using Banach’s fixed point theory. Also, the convergence and stability of the solution and the stability of the error are discussed. Several examples are given to illustrate the applicability of the presented method. The Maple program obtains all the results. A numerical simulation is carried out to determine the efficacy of the methodology, and the results are given in symmetrical forms. From the numerical results, it is noted that there is a symmetry utterly identical to the kernel used when replacing each x with y. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk)
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