B-metric Spaces Research Articles

Retracted: On Fuzzy Fixed-Point Results in Complex Valued Extended b-Metric Spaces with Application

Retracted: On Fuzzy Fixed-Point Results in Complex Valued Extended <i>b</i>-Metric Spaces with Application

Some Results in Fuzzy b-Metric Space with b-Triangular Property and Applications to Fredholm Integral Equations and Dynamic Programming

In this paper, we introduce the b-triangular property in fuzzy b-metric space. Furthermore, we give some new fixed point results in fuzzy b-metric space for non-continuous mappings. Our results generalize and expand some results from the related literature. Two applications of our results, to solving Fredholm integral equation and in dynamic programming, are also given.

Fixed-Point Theorems on Fuzzy Bipolar b-Metric Spaces

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.

On Topological and Metric Properties of ⊕-sb-Metric Spaces

In this paper, we study ⊕-sb-metric spaces, which were introduced to generalize the concept of strong b-metric spaces. In particular, we study the properties of the topology induced via an ⊕-sb metric (separation properties, countability axioms, etc.), prove the continuity of the ⊕-sb-metric, establish the metrizability of the ⊕-sb-metric spaces of countable weight, discuss the convergence structure of an ⊕-sb-metric space and prove the Baire category type theorem for such spaces. Most of the results obtained here are new already for strong b-metric spaces, i.e., in the case where an arithmetic sum “+” is taken in the role of ⊕.

Some new coupled fixed point results in complex value b-metric spaces

Some new coupled fixed point results in complex value b-metric spaces

Existence of Fuzzy Fixed Points and Common Fuzzy Fixed Points for FG-Contractions with Applications

This article contains results of the existence of fuzzy fixed points of fuzzy mappings that satisfy certain contraction conditions using the platform of partial b-metric spaces. Some non-trivial examples are provided to authenticate the main results. The constructed results in this work will likely stimulate new research directions in fuzzy fixed-point theory and related hybrid models. Eventually, some fixed-point results on multivalued mappings are established. These theorems provide an excellent application of main theorems on fuzzy mappings. The results of this article are extensions of many already existing results in the literature.

Stability analysis for complex-valued neural networks with fractional order

In the context of complex-valued rectangular b-metric spaces, the present study investigates the stability of complex-valued neural networks (CVNNs) with fractional order. Using the generalized contraction principle, we address the suitable condition for uniform stability of fractionally ordered CVNNs and establish the existence and uniqueness of the equilibrium point. Few numerical results are presented to show the feasibility and correctness of the results presented.

Fixed Point Results in Neutrosophic Rectangular Extended b-Metric Spaces

In this manuscript, we establish the notion of neutrosophic rectangular extended b-metric spaces and derive some fixed point results for contraction mappings. Also, we provide several non-trivial examples. Our results are more generalized with respect to the existing ones in the literature. At the end of the paper, we provide an application to non-linear fractional differential equations to test the validity of the results.

Some fixed point results for nonlinear $F$-type contractions in strong partial b-metric spaces

In this article, we demonstrate some fixed point results that generalises the Banachcontraction principle in a different way from the previously established literature findings. Weprovide some fixed point findings for non linear F type contractions in Strong Partial b-MetricSpaces (SPbMS). We also include some examples that demonstrates the applicability of ourfindings.

Further investigation on fixed point theorems via C-class functions in extended b-metric spaces

The purpose of this research project is to develop new theories, discuss, and extend some recent common fixed point results established when the underlying ambient space is an extended b-metric space and the contraction condition involves a new class of ψ-φ-C-contraction type mappings where ψ is the altering distance function and φ is the ultra-altering distance function. The unique fixed point theorems for such mappings in the setting of ψ-φ-complete metric spaces are proven. We also prove the fixed point theorem in partially ordered metric spaces. Moreover, some examples supporting the main results are given. Our results extend and generalize corresponding results in the literature. The start of the development of the theory of fixed points is tied to the end of the 19th century. The method of successive approximations is used in order to prove the solution's existence and uniqueness at the beginning of differential and integral equations. This branch of nonlinear analysis has been developed through various classes of spaces, such as metric spaces, topological spaces, probabilistic metric spaces, fuzzy metric spaces, and others. In developing the theory of fixed points, achievements are applied in various sciences, such as optimization, economics, and approximation theory. A very important step in the development of fixed point theory was taken by A.H. Ansari through the introduction of a C-class function. Using C-class functions, we generalize some known fixed point results, and Kamran et al. introduced a new intuitive concept of distance measure to extend the notion of b-metric space by further weakening the triangle inequality.

On extended, and extended rectangular, Menger probabilistic b-metric spaces: applications to the existence of solutions of integral, and fractional differential, equations

On extended, and extended rectangular, Menger probabilistic b-metric spaces: applications to the existence of solutions of integral, and fractional differential, equations

Rational Type Contraction in b-Metric Spaces and Common Coupled Fixed Point Theorems

Rational Type Contraction in b-Metric Spaces and Common Coupled Fixed Point Theorems

Almost Ćirić Type Contractions and Their Applications in Complex Valued b-Metric Spaces

In this article, we present the use of a unique and common fixed point for a pair of mappings that satisfy certain rational-type inequalities in complex-valued b-metric spaces. We also provide applications related to authenticity concerns in integral equations. Our results combine well-known contractions, such as the Ćirić contraction and almost contractions.

Computation and convergence of fixed points in graphical spaces with an application to elastic beam deformations

This paper aims to discuss the convergence behavior of fixed points for graphical Bc-Kannan-contractions using numerical iterations within the structure of graphical extended b-metric spaces. We provide innovative fixed point results using Bc-Kannan-contraction and demonstrate that every Kannan contraction is a graphical Bc-Kannan, but the converse is not valid in general. The findings, which explain the convergence of fixed points for graph-Kannan mappings, are the first of their kind in state of the art. We give examples using the framework of graphical analysis to show that our important findings are more general than the research that backs them up. Lastly, utilizing our results, we show that a solution to a fourth-order two-point boundary value problem expressing elastic beam deformations exists.

Teori Titik Tetap untuk Tipe Kannan yang Diperumum dalam Ruang b-Metrik Modular Lengkap

Some generalizations of Banach's contraction principle, which is a fixed-point theorem for contraction mapping in metric spaces, have developed rapidly in recent years. Some of the things that support the development of generalization are the emergence of mappings that are more general than contraction mappings and the emergence of spaces that are more general than metric spaces. The generalized Kannan type mappings are one of the mappings that are more general than contraction mappings. Furthermore, some of the more general spaces than metric spaces are b-metric spaces and modular b-metric spaces, which bring the concept of b-metric spaces into modular spaces. The fixed-point theorems for generalized Kannan-type mappings on b-metric spaces have been given. Therefore, this research aims to define generalized Kannan-type mappings on modular b-metric spaces and provide fixed point theorems for the generalized Kannan-type mappings on complete modular b-metric spaces. The definition of generalized Kannan type mapping in modular b-metric spaces is given by generalizing generalized Kannan type mappings in b-metric spaces. Then, the proof of fixed-point theorems for that mapping in modular b-metric spaces is carried out analogously to the proof of the fixed-point theorems for that mapping given in b-metric space. In this article, we obtain the definition of Kannan-type mappings and fixed-point theorems for generalized Kannan-type mappings in modular b-metric spaces and some consequences of the fixed-point theorem. In proving the theorem, a property of altering distance functions in b-metric spaces is generalized into modular b-metric spaces.

New Fixed Point Results in Neutrosophic b-Metric Spaces With Application

In this manuscript, we establish the notion of neutrosophic b-metric spaces as a generalization of fuzzy b-metric spaces, intuitionistic fuzzy b-metric spaces and neutrosophic metric spaces in which three symmetric properties plays an important role for membership, non-membership and neutral functions as well we derive some common fixed point and coincident point results for contraction mappings. Also, we provide several non-trivial examples with graphical views of neutrosophic b-metric spaces and contraction mappings by using computational techniques. Our results are more generalized with respect to the existing ones in the literature. At the end of the paper, we provide an application to test the validity of the main result.

Multivalued Common Fixed Points Theorem in Complex b-Metric Spaces

Multivalued Common Fixed Points Theorem in Complex b-Metric Spaces

Solving Integral Equations via Fixed Point Results Involving Rational-Type Inequalities

In this study, we establish unique and common fixed point results in the context of a complete complex-valued b-metric space using rational-type inequalities. The presented work generalizes some well-known results from the existing literature. Furthermore, to ensure the validity of the findings, we have included some examples and a section on the existence of solutions for the systems of Volterra–Hammerstein integral equations and Urysohn integral equations, respectively.

Fixed point theorems on product of b-metric spaces

The aim of this paper is to extend some fixed point results from [Serban, M. A., Teoria punctului fix pentru operatori definiti pe produs cartezian, Presa Universitar˘a Clujeana Cluj–Napoca, 2002] and [Presic, S. B., Sur une classe d’ inequations aux differences finite et sur la convergence de certaines suites, Publ. Inst. Math. (Beograd) (N. S.). 5(19) (1965), 75-78] in the framework of b-metric spaces.

The Results of Common Fixed Points in b-Metric Spaces

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 lp spaces, (p∈(0,1)), where we use the obtained results.