Contractive conditions in b-metric spaces (original) (raw)

A New Class of Contraction inb-Metric Spaces and Applications

Abstract and Applied Analysis, 2017

A novel class ofα-β-contraction for a pair of mappings is introduced in the setting ofb-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation.

Notes on Some Recent Papers Concerning FFF-Contractions in bbb-Metric Spaces

Constructive Mathematical Analysis, 2018

In several recent papers, attempts have been made to apply Wardowski's method of F-contractions in order to obtain fixed point results for single and multivalued mappings in b-metric spaces. In this article, it is shown that in most cases the conditions imposed on respective mappings are too strong and that the results can be obtained directly, i.e., without using most of the properties of auxiliary function F .

Contraction conditions using comparison functions on b-metric spaces

Fixed Point Theory and Applications, 2014

In this paper, we consider the setting of b-metric spaces to establish results regarding the common fixed points of two mappings, using a contraction condition defined by means of a comparison function. An example is presented to support our results comparing with existing ones. MSC:49H09, 47H10.

Generalization Contractive Mappings on Rectangular b-Metric Space

Hindawi Advances in Mathematical Physics, 2022

In this paper, we introduce new coincidence fixed point theorems for generalized ðϕ, ψÞ-contractive mappings fulfilling kind of an admissibility provision in a Hausdorff b-rectangular metric space with the support of C-functions. We applied our results to establish the existence of a solution for some integralitions. Finally, an example is presented to clarify our theorem.

Some Fixed Point Results in b-Metric Spaces and b-Metric-Like Spaces with New Contractive Mappings

Axioms

The aim of our paper is to present a new class of functions and to define some new contractive mappings in b-metric spaces. We establish some fixed point results for these new contractive mappings in b-metric spaces. Furthermore, we extend our main result in the framework of b-metric-like spaces. Some consequences of main results are also deduced. We present some examples to illustrate and support our results. We provide an application to solve simultaneous linear equations. In addition, we present some open problems.

Rectangular b-Metric Spaces and Contraction Principle

The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular metric space and b-metric space. An analogue of Banach contraction principle and Kannan's fixed point theorem is proved in this space. Our result generalizes many known results in fixed point theory.

New theorems on extended b-metric spaces under new contractions

Nonlinear Analysis: Modelling and Control

The notion of extended b-metric space plays an important role in the field of applied analysis to construct new theorems in the field of fixed point theory. In this paper, we construct and prove new theorems in the filed of fixed point theorems under some new contractions. Our results extend and modify many existing results in the literature. Also, we provide an example to show the validity of our results. Moreover, we apply our result to solve the existence and uniqueness of such equations.

On Nonlinear Contractions in New Extended b-Metric Spaces

2019

Very recently, the notion of extended b-metric spaces was introduced by replacing the modified triangle inequality with a functional triangle inequality and the analog of the renowned Banach fixed point theorem was proved in this new structure. In this paper, continuing in this direction, we further refine the functional inequality and establish some fixed point results for nonlinear contractive mappings in the new setting. A nontrivial example for the new extended b-metric space is given.

Some remarks on contraction mappings in rectangular b-metric spaces

Boletim da Sociedade Paranaense de Matemática, 2021

In this paper, we give a short proof for Reich contraction in rectangular b-metric spaces with increased range of the Lipschtzian constants and illustrate this with a suitable example. Our results generalize, improve and complement several ones in the existing literature.