Mappings In B-metric Spaces Research Articles

Integral Operators in b-Metric and Generalized b-Metric Spaces and Boundary Value Problems

We study fixed-point theorems of contractive mappings in b-metric space, cone b-metric space, and the newly introduced extended b-metric space. To generalize an existence and uniqueness result for the so-called Φs functions in the b-metric space to the extended b-metric space and the cone b-metric space, we introduce the class of ΦM functions and apply the Hölder continuous condition in the extended b-metric space. The obtained results are applied to prove the existence and uniqueness of solutions and positive solutions for nonlinear integral equations and fractional boundary value problems. Examples and numerical simulation are given to illustrate the applications.

Existence of solution of a system of non-linear differential inclusions with non-local, integral boundary conditions via fixed points of hybrid contractions

In the present article, we have introduced the notions of γ-admissibility for the pair of q-ROF set-valued maps and admissible hybrid q-ROF Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{Z}$\\end{document}-contraction. Notions introduced in the article generalizes the existing concepts in fuzzy literature. Common fixed point result for a pair of γ-admissible q-ROF mappings in b-metric spaces utilizing the introduced contraction is presented. A nontrivial example to support the obtained results is also included. As an application, we have discussed the existence of solution of system of non-linear n-th order differential inclusions with non-local and integral boundary conditions.

Fixed point results for Geraghty–Ćirić-type contraction mappings in b-metric space with applications

In this study, we manifest a new class of mappings that satisfy Geraghty–Ćirić-type contractive conditions in the context of b-metric spaces and prove a theorem on the existence and uniqueness of fixed points. Our results unify and generalize the results of Geraghty; Ćirić; Dukic, Kadelburg, and Radenović; and Shu-fang Li, Fei Hi, and Ning Lu in the setting of b-metric spaces. Furthermore, we provide examples to verify the correctness and applicability of our results. We also utilize our findings to show the existence of a unique solution for a nonlinear integral equation.

A New Fixed-Point Theorem in b-Metric Space with Application

The goal of this study is to provide a new contraction mapping in b-metric space. We build a fixed point result for this new contraction mapping; we also provide applications related to authenticity concerns in integral equations.

A new approach to coincidence points and common fixed points under a homotopy of families of mappings in b-metric spaces

In this paper, we derive coincidence point and common fixed point results under order homotopies of families of mappings in partially ordered [Formula: see text]-metric spaces.

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.

Fixed Point Theorems of Almost Generalized Contractive Mappings in b-Metric Spaces and an Application to Integral Equation

In this study, we have new fixed point results for weak contraction mappings in complete and partially ordered b-metric spaces. Our findings expand and generalize the results of Jachymski and Mituku et al and many more results in the literature as well. To illustrate our work, we present an application on the existence and uniqueness of a nonlinear quadratic integral problem solution. Moreover, an open problem is presented to enable the scope for future research in this area.

Fixed Point Results of Rational Type-contraction Mapping in b-Metric Spaces with an Application

In this article, we establish the existence of fixed points of rational type contractions in the setting of b-metric spaces and we verify the T-stability of the P property for some mappings. Also, we present a few examples to illustrate the validity of the results obtained in the paper. Finally, results are applied to find the solution for an integral equation.

Fixed point theorems for extended interpolative multi-valued non-self mappings in b-metric space with some application

Fixed point theorems for extended interpolative multi-valued non-self mappings in b-metric space with some application

A generalized common fixed point of multi-valued maps in b-metric space

In this work we are interested to prove a general fixed point theorem for a pair of multi-valued mappings in b-metric spaces. The results in this paper generalize the results obtained in [19] and to obtain other particular results.

Some Boyd–Wong contraction type mappings in b-metric spaces

Some Boyd–Wong contraction type mappings in b-metric spaces

Common Best Proximity Point Theorems for Generalized Proximal Weakly Contractive Mappings in b-Metric Space

In this paper, common best proximity point theorems for weakly contractive mapping in b-metric spaces in the cases of nonself-mappings are proved; we introduced the notion of generalized proximal weakly contractive mappings in b-metric spaces and proved the existence and uniqueness of common best proximity point for these mappings in complete b-metric spaces. We also included some supporting examples that our finding is more generalized with the references we used.

Fixed point theorems for $$\left( \chi ,F\right)$$-Dass–Gupta contraction mappings in b-metric spaces with applications to integral equations

Fixed point theorems for $$\left( \chi ,F\right)$$-Dass–Gupta contraction mappings in b-metric spaces with applications to integral equations

The Results on Coincidence and Common Fixed Points for a New Type Multivalued Mappings in b-Metric Spaces

In this paper, we obtain the results of coincidence and common fixed points in b-metric spaces. We work with a new type of multivalued quasi-contractive mapping with nonlinear comparison functions. Our results generalize and improve several recent results. Additionally, we give an application of the obtained results to dynamical systems.

Existence of solutions for boundary value problems and nonlinear matrix equations via F-contraction mappings in b-metric spaces

The purpose of this paper is to present some sufficient conditions for the existence of solutions for nonlinear matrix equations and the second-order two-point boundary value problems for nonlinear ordinary differential equations via fixed point theorem. To do this, we introduce two classes of mappings called the Suzuki–Geraghty-[Formula: see text]-[Formula: see text]-contraction mappings and generalize Suzuki-type [Formula: see text]-F-contraction mappings and establish some fixed point results for these classes of mappings. The results obtained in this work complements, extends, generalizes, and improves some known results in the literature.

Fixed Point Theorems for (,) Type Expansive Mappings in b-Metric Spaces

Fixed Point Theorems for (,) Type Expansive Mappings in b-Metric Spaces

New generalized rational α∗-contraction for multivalued mappings in b-metric space

In this paper, we introduce the concept of generalized rational α ∗ -contraction for multivalued mappings in the setting of b-metric space. Further, we prove some common fixed point theorems for such rational contraction of multivalued mappings.

Fixed Point Theorems for α , k , θ , φ -Contraction Multivalued Mappings in b -Metric Space

We present the concept of α , k , θ , φ -contractive multivalued mappings in b -metric spaces and prove some fixed point results for these mappings in this study. Our results expand and refine some of the literature’s findings in fixed point theory.

Fixed point theorems for (α,β)-(φ,ψ)-rational contractive type mappings

In this paper, we introduce the concept of (α,β)-(φ,ψ)-rational contractive mapping in b-metric spaces. We establish some fixed point theorems for such mappings and also give an application supporting our results.

Common fixed point theorems for multivalued mappings in b-metric spaces with an application to integral inclusions

Common fixed point theorems for multivalued mappings in b-metric spaces with an application to integral inclusions