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25 pages, 350 KB

Open AccessArticle

Fixed-Point Results with Applications in Generalized Neutrosophic Rectangular b-Metric Spaces

by Nawab Hussain, Nawal Alharbi and Ghada Basendwah

Axioms 2024, 13(12), 818; https://doi.org/10.3390/axioms13120818 - 24 Nov 2024

Cited by 1 | Viewed by 714

In this paper, we introduce several new concepts: generalized neutrosophic rectangular b-metric-like spaces (GNRBMLSs), generalized intuitionistic rectangular b-metric-like spaces (GIRBMLSs), and generalized fuzzy rectangular b-metric-like spaces (GFRBMLSs). These innovative spaces can expand various topological spaces, including neutrosophic rectangular extended b [...] Read more.

In this paper, we introduce several new concepts: generalized neutrosophic rectangular b-metric-like spaces (GNRBMLSs), generalized intuitionistic rectangular b-metric-like spaces (GIRBMLSs), and generalized fuzzy rectangular b-metric-like spaces (GFRBMLSs). These innovative spaces can expand various topological spaces, including neutrosophic rectangular extended b-metric-like spaces, intuitionistic fuzzy rectangular extended b-metric-like spaces, and fuzzy rectangular extended b-metric-like spaces. Moreover, we establish Banach’s fixed point theorem and Ćirić’s quasi-contraction theorem with respect to these spaces, and we explore an application regarding the existence and uniqueness of solutions for fuzzy fractional delay integro-differential equations, as derived from our main results. Full article

(This article belongs to the Special Issue Fixed Point Theory and Its Applications)

14 pages, 390 KB

Open AccessArticle

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

Cited by 2 | Viewed by 1457

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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30 pages, 368 KB

Open AccessArticle

Fuzzy Triple Controlled Metric like Spaces with Applications

by Naeem Saleem, Salman Furqan, Kinda Abuasbeh and Muath Awadalla

Mathematics 2023, 11(6), 1390; https://doi.org/10.3390/math11061390 - 13 Mar 2023

Cited by 5 | Viewed by 1984

Abstract

In this article, we introduce the concept of a fuzzy triple controlled metric like space in the sense that the self distance may not be equal to one. We have used three functions in our space that generalize fuzzy controlled rectangular, extended fuzzy [...] Read more.

In this article, we introduce the concept of a fuzzy triple controlled metric like space in the sense that the self distance may not be equal to one. We have used three functions in our space that generalize fuzzy controlled rectangular, extended fuzzy rectangular, fuzzy

b -

rectangular and fuzzy rectangular metric like spaces. Various examples are given to justify our definitions and results. As for the topological aspect, we prove a fuzzy triple controlled metric like space is not Hausdorff. We also apply our main result to solve the uniqueness of the solution of a fractional differential equation. Full article

(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)

12 pages, 297 KB

Open AccessArticle

Solving a System of Integral Equations in Rectangular Menger Probabilistic Metric Spaces and Rectangular Menger Probabilistic b-Metric Spaces

by Ehsan Lotfali Ghasab, Reza Chaharpashlou and António M. Lopes

Symmetry 2023, 15(1), 70; https://doi.org/10.3390/sym15010070 - 27 Dec 2022

Cited by 3 | Viewed by 1981

Abstract

This work introduces the concepts of rectangular Menger probabilistic metric (

R M P M

) space and rectangular Menger probabilistic b-metric (

R M P b M

) space as generalizations of the Menger probabilistic metric space and the Menger probabilistic [...] Read more.

This work introduces the concepts of rectangular Menger probabilistic metric (

R M P M

) space and rectangular Menger probabilistic b-metric (

R M P b M

) space as generalizations of the Menger probabilistic metric space and the Menger probabilistic b-metric space, respectively. Some nonunique fixed-point and coupled-fixed-point results for contractive mappings are provided. The findings extend and improve outcomes presented in the existing literature. The main results are illustrated with examples, and validated by means of an application to a system of integral equations. The importance of spaces with non-Hausdorff topology is high, as is the case of computer science, with the Tarskian approach to programming language semantics. Full article

(This article belongs to the Special Issue Symmetry in Functional Equations: Methods, Applications and Mathematical Models)

23 pages, 377 KB

Open AccessArticle

Relation-Theoretic Coincidence and Common Fixed Point Results in Extended Rectangular b-Metric Spaces with Applications

by Yan Sun and Xiaolan Liu

Symmetry 2022, 14(8), 1588; https://doi.org/10.3390/sym14081588 - 2 Aug 2022

Cited by 2 | Viewed by 1775

Abstract

The objective of this paper is to obtain new relation-theoretic coincidence and common fixed point results for some mappings F and g via hybrid contractions and auxiliary functions in extended rectangular b-metric spaces, which improve the existing results and give some relevant [...] Read more.

The objective of this paper is to obtain new relation-theoretic coincidence and common fixed point results for some mappings F and g via hybrid contractions and auxiliary functions in extended rectangular b-metric spaces, which improve the existing results and give some relevant results. Finally, some nontrivial examples and applications to justify the main results. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis)

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22 pages, 328 KB

Open AccessArticle

On Fuzzy Extended Hexagonal b-Metric Spaces with Applications to Nonlinear Fractional Differential Equations

by Sumaiya Tasneem Zubair, Kalpana Gopalan, Thabet Abdeljawad and Bahaaeldin Abdalla

Symmetry 2021, 13(11), 2032; https://doi.org/10.3390/sym13112032 - 27 Oct 2021

Cited by 7 | Viewed by 2028

Abstract

The focus of this research article is to investigate the notion of fuzzy extended hexagonal b-metric spaces as a technique of broadening the fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces as well as to derive the Banach [...] Read more.

The focus of this research article is to investigate the notion of fuzzy extended hexagonal b-metric spaces as a technique of broadening the fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces as well as to derive the Banach fixed point theorem and several novel fixed point theorems with certain contraction mappings. The analog of hexagonal inequality in fuzzy extended hexagonal b-metric spaces is specified as follows utilizing the function

b (c, d)

:

m_{h} (c, d, t + s + u + v + w) \geq m_{h} (c, e, \frac{t}{b (c, d)}) * m_{h} (e, f, \frac{s}{b (c, d)}) * m_{h} (f, g, \frac{u}{b (c, d)}) * m_{h} (g, k, \frac{v}{b (c, d)}) * m_{h} (k, d, \frac{w}{b (c, d)})

for all

t, s, u, v, w > 0

and

c \neq e, e \neq f, f \neq g, g \neq k, k \neq d

. Further to that, this research attempts to provide a feasible solution for the Caputo type nonlinear fractional differential equations through effective applications of our results obtained. Full article

(This article belongs to the Section Mathematics)

18 pages, 315 KB

Open AccessArticle

Fixed Point Results via α-Admissibility in Extended Fuzzy Rectangular b-Metric Spaces with Applications to Integral Equations

by Badshah-e-Rome, Muhammad Sarwar and Rosana Rodríguez-López

Mathematics 2021, 9(16), 2009; https://doi.org/10.3390/math9162009 - 22 Aug 2021

Cited by 11 | Viewed by 2307

Abstract

In this article, the concept of extended fuzzy rectangular b-metric space (EFR_bMS, for short) is initiated, and some fixed point results frequently used in the literature are generalized via α-admissibility in the setting of EFR_bMS. For the [...] Read more.

In this article, the concept of extended fuzzy rectangular b-metric space (EFR_bMS, for short) is initiated, and some fixed point results frequently used in the literature are generalized via α-admissibility in the setting of EFR_bMS. For the illustration of the work presented, some supporting examples and an application to the existence of solutions for a class of integral equations are also discussed. Full article

(This article belongs to the Special Issue New Trends on Boundary Value Problems)

8 pages, 278 KB

Open AccessArticle

Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space

by Pragati Gautam, Luis Manuel Sánchez Ruiz and Swapnil Verma

Symmetry 2021, 13(1), 32; https://doi.org/10.3390/sym13010032 - 28 Dec 2020

Cited by 19 | Viewed by 3036

Abstract

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the [...] Read more.

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result. Full article

(This article belongs to the Special Issue Advanced Calculus in Problems with Symmetry)

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6 pages, 224 KB

Open AccessArticle

On a Common Jungck Type Fixed Point Result in Extended Rectangular b-Metric Spaces

by Hassen Aydi, Zoran D. Mitrović, Stojan Radenović and Manuel de la Sen

Axioms 2020, 9(1), 4; https://doi.org/10.3390/axioms9010004 - 27 Dec 2019

Cited by 6 | Viewed by 2921

Abstract

In this paper, we present a Jungck type common fixed point result in extended rectangular b-metric spaces. We also give some examples and a known common fixed point theorem in extended b-metric spaces. Full article

(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics II)

15 pages, 282 KB

Open AccessArticle

Extended Rectangular M_rξ-Metric Spaces and Fixed Point Results

by Mohammad Asim, Kottakkaran Sooppy Nisar, Ahmed Morsy and Mohammad Imdad

Mathematics 2019, 7(12), 1136; https://doi.org/10.3390/math7121136 - 21 Nov 2019

Cited by 10 | Viewed by 2228

Abstract

In this paper, we enlarge the classes of rectangular

M_{b}

-metric spaces and extended rectangular b-metric spaces by considering the class of extended rectangular

M_{r ξ}

-metric spaces and utilize the same to prove an analogue of Banach contraction principle [...] Read more.

In this paper, we enlarge the classes of rectangular

M_{b}

-metric spaces and extended rectangular b-metric spaces by considering the class of extended rectangular

M_{r ξ}

-metric spaces and utilize the same to prove an analogue of Banach contraction principle in such 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 solution for a system of Fredholm integral equation. Full article

(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)

17 pages, 332 KB

Open AccessArticle

Extended Rectangular b-Metric Spaces and Some Fixed Point Theorems for Contractive Mappings

by Zead Mustafa, Vahid Parvaneh, Mohammed M.M. Jaradat and Zoran Kadelburg

Symmetry 2019, 11(4), 594; https://doi.org/10.3390/sym11040594 - 24 Apr 2019

Cited by 28 | Viewed by 4867

Abstract

In this paper, we introduce the class of extended rectangular b-metric spaces as a generalization of both rectangular metric and rectangular b-metric spaces. In addition, some fixed point results connected with certain contractions are obtained and examples are given to illustrate [...] Read more.

In this paper, we introduce the class of extended rectangular b-metric spaces as a generalization of both rectangular metric and rectangular b-metric spaces. In addition, some fixed point results connected with certain contractions are obtained and examples are given to illustrate these results. Full article

(This article belongs to the Special Issue Symmetric and non-symmetric contractions in various abstract spaces)

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