Symmetry

Research

13 pages, 285 KiB

Open AccessArticle

Fixed Point Theorems in Symmetric Controlled M-Metric Type Spaces

by Khaled Suwais, Nihal Taş, Nihal Özgür and Nabil Mlaiki

Symmetry 2023, 15(9), 1665; https://doi.org/10.3390/sym15091665 - 29 Aug 2023

Cited by 5 | Viewed by 983

One of the frequently studied approaches in metric fixed-point theory is the generalization of the used metric space. Under this approach, in this study, we introduce a new extension of M-metric spaces, called controlled M-metric spaces, achieved by modifying the triangle [...] Read more.

One of the frequently studied approaches in metric fixed-point theory is the generalization of the used metric space. Under this approach, in this study, we introduce a new extension of M-metric spaces, called controlled M-metric spaces, achieved by modifying the triangle inequality and keeping the symmetric condition of the space. The investigation focuses on exploring fundamental properties of this newly defined space, incorporating topological aspects. Several fixed-point theorems and fixed-circle results are established within these spaces complemented by illustrative examples to demonstrate the implications of our findings. Moreover, we present an application involving high-degree polynomial equations. Full article

(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)

16 pages, 330 KiB

Open AccessArticle

Some Fixed-Point Results for the KF-Iteration Process in Hyperbolic Metric Spaces

by Aynur Şahin, Emre Öztürk and Gaurav Aggarwal

Symmetry 2023, 15(7), 1360; https://doi.org/10.3390/sym15071360 - 4 Jul 2023

Cited by 5 | Viewed by 2074

Abstract

In this paper, we modify the

K F

-iteration process into hyperbolic metric spaces where the symmetry condition is satisfied and establish the weak

w^{2}

-stability and data dependence results for contraction mappings. We also prove some

Δ

-convergence and strong convergence [...] Read more.

In this paper, we modify the

K F

-iteration process into hyperbolic metric spaces where the symmetry condition is satisfied and establish the weak

w^{2}

-stability and data dependence results for contraction mappings. We also prove some

Δ

-convergence and strong convergence theorems for generalized

(α, β)

-nonexpansive type 1 mappings. Finally, we offer a numerical example of generalized

(α, β)

-nonexpansive type 1 mappings and show that the

K F

-iteration process is more effective than some other iterations. Our results generalize and improve several relevant results in the literature. Full article

(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)

► Show Figures

Figure 1

12 pages, 297 KiB

Open AccessArticle

The Results of Common Fixed Points in b-Metric Spaces

by Ivan D. Aranđelović, Zoran D. Mitrović, Ahmad Aloqaily and Nabil Mlaiki

Symmetry 2023, 15(7), 1344; https://doi.org/10.3390/sym15071344 - 30 Jun 2023

Cited by 1 | Viewed by 1192

Abstract

In this paper, we present some results on the existence and uniqueness of common fixed points on

d^{*}

-complete topological spaces. Our results generalize and improve upon earlier results in the literature. Finally, we give some examples in

l_{p}

spaces, [...] Read more.

In this paper, we present some results on the existence and uniqueness of common fixed points on

d^{*}

-complete topological spaces. Our results generalize and improve upon earlier results in the literature. Finally, we give some examples in

l_{p}

spaces,

(p \in (0, 1))

, where we use the obtained results. Full article

(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)

17 pages, 338 KiB

Open AccessArticle

Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems

by Naeem Saleem, Bilal Iqbal, Fady Hasan and Wasfi Shatanawi

Symmetry 2023, 15(6), 1162; https://doi.org/10.3390/sym15061162 - 27 May 2023

Cited by 2 | Viewed by 999

Abstract

The purpose of this paper is to define the notion of extended convex ℱ contraction by imposing less conditions on the function ℱ satisfying certain contractive conditions. We prove the existence of fixed points for these types of mappings in the setting of [...] Read more.

The purpose of this paper is to define the notion of extended convex ℱ contraction by imposing less conditions on the function ℱ satisfying certain contractive conditions. We prove the existence of fixed points for these types of mappings in the setting of b-metric spaces. In addition, some illustrative examples are provided to show the usability of the obtained results. Lastly, we use the obtained fixed-point results to find the fractals with respect to the iterated function systems in the framework of b-metric spaces. Furthermore, the variables involved in the b-metric space are symmetric, and symmetry plays an important role in solving the nonlinear problems defined in operator theory. Full article

(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)

11 pages, 269 KiB

Open AccessArticle

Controlled S-Metric-Type Spaces and Applications to Fractional Integrals

by Nilay Ekiz Yazici, Ozgur Ege, Nabil Mlaiki and Aiman Mukheimer

Symmetry 2023, 15(5), 1100; https://doi.org/10.3390/sym15051100 - 17 May 2023

Cited by 3 | Viewed by 1303

Abstract

In this paper, we introduce controlled S-metric-type spaces and give some of their properties and examples. Moreover, we prove the Banach fixed point theorem and a more general fixed point theorem in this new space. Finally, using the new results, we give two [...] Read more.

In this paper, we introduce controlled S-metric-type spaces and give some of their properties and examples. Moreover, we prove the Banach fixed point theorem and a more general fixed point theorem in this new space. Finally, using the new results, we give two applications on Riemann–Liouville fractional integrals and Atangana–Baleanu fractional integrals. Full article

(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)

16 pages, 325 KiB

Open AccessArticle

Some Common Fixed Circle Results on Metric and 𝕊-Metric Spaces with an Application to Activation Functions

by Nihal Taş, Elif Kaplan, Dania Santina, Nabil Mlaiki and Wasfi Shatanawi

Symmetry 2023, 15(5), 971; https://doi.org/10.3390/sym15050971 - 24 Apr 2023

Cited by 4 | Viewed by 1067

Abstract

In this paper, we modify various contractive conditions (C.C.)s such as Ciric type (C.C.), Rhoades type (C.C.), Seghal type (C.C.), Bianchini type (C.C.), and Berinde type (C.C.) for two self-mappings, considering that the contractive property plays a major role in establishing a fixed [...] Read more.

In this paper, we modify various contractive conditions (C.C.)s such as Ciric type (C.C.), Rhoades type (C.C.), Seghal type (C.C.), Bianchini type (C.C.), and Berinde type (C.C.) for two self-mappings, considering that the contractive property plays a major role in establishing a fixed circle (F.C.) on both metric spaces (M-s) and

S

-(M-s) where the symmetry condition is satisfied, and we utilize them to establish a common (F.C.). We prove new (F.C.) results on both (M-s) and

S

-(M-s) with illustrative examples. Finally, we provide an application to activation functions such as rectified linear unit activation functions and parametric rectified linear unit activation functions. Full article

(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)

► Show Figures

Figure 1

19 pages, 318 KiB

Open AccessArticle

Double-Controlled Quasi M-Metric Spaces

by Irshad Ayoob, Ng Zhen Chuan and Nabil Mlaiki

Symmetry 2023, 15(4), 893; https://doi.org/10.3390/sym15040893 - 10 Apr 2023

Viewed by 1225

Abstract

One of the well-studied generalizations of a metric space is known as a partial metric space. The partial metric space was further generalized to the so-called M-metric space. In this paper, we introduce the Double-Controlled Quasi M-metric space as a new [...] Read more.

One of the well-studied generalizations of a metric space is known as a partial metric space. The partial metric space was further generalized to the so-called M-metric space. In this paper, we introduce the Double-Controlled Quasi M-metric space as a new generalization of the M-metric space. In our new generalization of the M-metric space, the symmetry condition is not necessarily satisfied and the triangle inequality is controlled by two binary functions. We establish some fixed point results, along with the examples and applications to illustrate our results. Full article

(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)

12 pages, 283 KiB

Open AccessArticle

Fixed-Point Results for (α-ψ)-Fuzzy Contractive Mappings on Fuzzy Double-Controlled Metric Spaces

by Fatima M. Azmi

Symmetry 2023, 15(3), 716; https://doi.org/10.3390/sym15030716 - 13 Mar 2023

Cited by 3 | Viewed by 1246

Abstract

We introduce the novel concept of (

α

-

ψ

)-fuzzy contractive mappings on fuzzy double-controlled metric spaces and demonstrate some fixed-point results. The theorems presented generalize some intriguing findings in the literature. Thus, we prove the fixed-point theorem in the settings of [...] Read more.

We introduce the novel concept of (

α

-

ψ

)-fuzzy contractive mappings on fuzzy double-controlled metric spaces and demonstrate some fixed-point results. The theorems presented generalize some intriguing findings in the literature. Thus, we prove the fixed-point theorem in the settings of fuzzy double-controlled metric spaces. Furthermore, we provide several examples and an application of our result on the existence of the solution to an integral equation. Full article

(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)

12 pages, 277 KiB

Open AccessArticle

New Generalization of Metric-Type Spaces—Strong Controlled

by Dania Santina, Wan Ainun Mior Othman, Kok Bin Wong and Nabil Mlaiki

Symmetry 2023, 15(2), 416; https://doi.org/10.3390/sym15020416 - 4 Feb 2023

Cited by 1 | Viewed by 1468

Abstract

In this manuscript, we establish a new type of metric space that is called controlled strong metric spaces by introducing a controlled function to the triangle inequality as follows: [...] Read more.

In this manuscript, we establish a new type of metric space that is called controlled strong metric spaces by introducing a controlled function to the triangle inequality as follows:

℘ (s, r) \leq ℘ (s, z) + η (z, r) ℘ (z, r),

and keeping the symmetry condition that is

℘ (s, r) = ℘ (r, s) for all r, s

. We demonstrate the existence of the fixed point of self-mapping and its uniqueness in such spaces that satisfy linear and nonlinear contractions. Moreover, we provide three applications of results to polynomial equations of high degree, systems of linear equations, along with fractional differential equations. Full article

(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)

Journal Menu

Journal Browser

Symmetry Application in Fixed Point Theory

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (9 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI