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Symmetry
Special Issues
Elementary Fixed Point Theory and Common Fixed Points II
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Elementary Fixed Point Theory and Common Fixed Points II

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 3975

Special Issue Editors

Dr. Salvatore Sessa

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Guest Editor
Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
Interests: fuzzy relation equations; fixed point theory; geographical information systems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Mohammad Imdad

E-Mail Website
Guest Editor
Department of Mathematics, Aligarh Muslim University, Aligarh, India
Interests: fixed; point; theory
Special Issues, Collections and Topics in MDPI journals
Dr. Waleed Mohammad Alfaqih

E-Mail Website
Guest Editor
Department of Mathematics, Hajjah University, Hajjah, Yemen
Interests: fixed; point; theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In this Special Issue, we solicit contributions dealing with fixed-point theorems from a general point of view regarding original concepts or ideas into recent advances of this theory, avoiding any trivial extension of results already consolidated, possibly accompanied by concrete examples. We recommend to the authors to consider in the theorems symmetric inequalities or symmetric conditions with respect to the metric (or hyper-metric if multifunctions are involved) used, i.e., anyone can obtain a dual result by considering dual definitions based simply on the change of variables, inequality sign, etc.

For example, this happens mainly in common fixed-point theorems where the use of two (multi-)functions must be interchangeable, i.e., a concept depending on one of two functions must hold with respect to the other. Very often, looking at some of the papers published, if f and g are self-maps of a metric space, some definitions seem only dependent on f and do not hold if g should assume the same role as f. Our aim is to emphasize this aspect mainly in this journal whose title obliges us to keep in mind the above recommendation. Following this line of thought, common fixed-point theorems (which motivate the second part of the title of this Special Issue) are welcome in the context of general environments, but this aspect is left to the discretion of the authors.

Our aim is for this Special Issue to collect meaningful papers which give a jolt to this theory. Please note that all submissions need to fall within Symmetry’s scope.

Dr. Salvatore Sessa
Prof. Dr. Mohammad Imdad
Dr. Waleed Mohammad Alfaqih
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. 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.

Published Papers (5 papers)

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Research

12 pages, 263 KiB  
Article
An Existence Result for Second-Order Boundary-Value Problems via New Fixed-Point Theorems on Quasi-Metric Space
by Gonca Durmaz Güngör and Ishak Altun
Symmetry 2024, 16(1), 99; https://doi.org/10.3390/sym16010099 - 13 Jan 2024
Viewed by 633
Abstract
We introduce the new idea of (α−θσ)-contraction in quasi-metric spaces in this paper. For these kinds of mappings, we then prove new fixed-point theorems on left K, left M, and left [...] Read more.
We introduce the new idea of (α−θσ)-contraction in quasi-metric spaces in this paper. For these kinds of mappings, we then prove new fixed-point theorems on left K, left M, and left Smyth-complete quasi-metric spaces. We also apply our results to infer the existence of a solution to a second-order boundary-value problem. Full article
(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points II)
23 pages, 330 KiB  
Article
Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations
by Cemil Tunç, Fehaid Salem Alshammari and Fahir Talay Akyildiz
Symmetry 2023, 15(12), 2205; https://doi.org/10.3390/sym15122205 - 15 Dec 2023
Cited by 1 | Viewed by 721
Abstract
The authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton’s method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second [...] Read more.
The authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton’s method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second objective of the paper is to extend and improve some earlier results to nonlinear HTFIEs. The authors prove two new theorems with regard to the existence and uniqueness of solutions (EUSs) of HTFIEs via a technique called progressive contractions, which belongs to T. A. Burton, and the Chebyshev norm and complete metric. Full article
(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points II)
14 pages, 390 KiB  
Article
Exploring Fuzzy Triple Controlled Metric Spaces: Applications in Integral Equations
by Fatima M. Azmi
Symmetry 2023, 15(10), 1943; https://doi.org/10.3390/sym15101943 - 20 Oct 2023
Viewed by 654
Abstract
In this article, we delve into the study of fuzzy triple controlled metric spaces, investigating their properties and presenting a range of illustrative examples. We emphasize the broader applicability of this concept in comparison to fuzzy rectangular metric spaces and fuzzy rectangular b [...] Read more.
In this article, we delve into the study of fuzzy triple controlled metric spaces, investigating their properties and presenting a range of illustrative examples. We emphasize the broader applicability of this concept in comparison to fuzzy rectangular metric spaces and fuzzy rectangular b-metric spaces. By introducing the novel concept of (α-ψ)-fuzzy contractive mappings, we derive fixed point results specifically designed for complete fuzzy triple controlled metric spaces. Our theorems extend and enrich previous findings in this field. Additionally, we demonstrate the practical significance of our study by applying our findings to the solution of an integral equation and providing an example of its application. Furthermore, we propose potential avenues for future research endeavors. Full article
(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points II)
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17 pages, 303 KiB  
Article
Fixed-Point Theorems on Fuzzy Bipolar b-Metric Spaces
by Balaji Ramalingam, Ozgur Ege, Ahmad Aloqaily and Nabil Mlaiki
Symmetry 2023, 15(10), 1831; https://doi.org/10.3390/sym15101831 - 27 Sep 2023
Viewed by 621
Abstract
In this manuscript, we establish some fixed-point theorems without continuity by using the triangular property on a fuzzy bipolar b-metric space as a generalized version and expansion of the well-known results. We also provide some examples and applications of the integral equation [...] Read more.
In this manuscript, we establish some fixed-point theorems without continuity by using the triangular property on a fuzzy bipolar b-metric space as a generalized version and expansion of the well-known results. We also provide some examples and applications of the integral equation to the solution for our main results. Full article
(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points II)
16 pages, 328 KiB  
Article
Development of Fixed Point Results for αΓ-F-Fuzzy Contraction Mappings with Applications
by Salvatore Sessa, Fahad Jahangeer, Doha A. Kattan and Umar Ishtiaq
Symmetry 2023, 15(7), 1300; https://doi.org/10.3390/sym15071300 - 22 Jun 2023
Cited by 2 | Viewed by 830
Abstract
This manuscript contains several fixed point results for αΓ-F-fuzzy contractive mappings in the framework of orthogonal fuzzy metric spaces. The symmetric property guarantees that the distance function is consistent and does not favour any one direction in orthogonal fuzzy [...] Read more.
This manuscript contains several fixed point results for αΓ-F-fuzzy contractive mappings in the framework of orthogonal fuzzy metric spaces. The symmetric property guarantees that the distance function is consistent and does not favour any one direction in orthogonal fuzzy metric spaces. No matter how the points are arranged, it enables a fair assessment of the separations between all of them. In fixed point results, the symmetry condition is preserved for several types of contractive self-mappings. Moreover, we provide several non-trivial examples to show the validity of our main results. Furthermore, we solve non-linear fractional differential equations, the Atangana–Baleanu fractional integral operator and Fredholm integral equations by utilizing our main results. Full article
(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points II)
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