Fixed point theorems for generalized $(\alpha ,\psi )$-contraction mappings in rectangular quasi b-metric spaces

Fixed Point Theory and Applications Pub Date : 2022-05-02 DOI:10.1186/s13663-022-00723-w

Abagaro, Bontu Nasir, Tola, Kidane Koyas, Mamud, Mustefa Abduletif

引用次数: 1

Abstract

In this paper, we introduce the class of rectangular quasi b-metric spaces as a generalization of rectangular metric spaces, rectangular quasi-metric spaces, rectangular b-metric spaces, define generalized $(\alpha ,\psi ) $ -contraction mappings and study fixed point results for the maps introduced in the setting of rectangular quasi b-metric spaces. Our results extend and generalize related fixed point results in the literature, in particular, the works of Karapinar and Lakzian (J. Funct. Spaces 2014:914398, 2014), Alharbi et al. (J. Math. Anal. 9(3):47–60, 2018), and Khuangsatung et al. (Thai J. Math. 2020:89–101, 2020) from rectangular quasi metric space and rectangular b-metric space to rectangular quasi b-metric spaces. We also provide examples in support of our main findings. Furthermore, we applied one of our results to determine the existence of a solution to an integral equation.

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矩形拟b-度量空间中广义$(\alpha ,\psi )$ -收缩映射的不动点定理

本文引入了矩形拟b-度量空间，作为矩形度量空间、矩形拟度量空间、矩形b-度量空间的推广，定义了广义$(\alpha ,\psi ) $ -收缩映射，研究了在矩形拟b-度量空间设置下引入的映射的不动点结果。我们的结果扩展和推广了文献中的相关不动点结果，特别是Karapinar和Lakzian (J. Funct)的作品。[j] .中国科学:自然科学，2014 (4):914 - 398 .][j] .数学学报，2018,39 (3):47 - 60,2018)，Khuangsatung et al. (Thai J. Math. 2020:89 - 101,2020)从矩形准度量空间和矩形b度量空间到矩形准b度量空间。我们还提供了一些例子来支持我们的主要发现。进一步，我们应用我们的一个结果来确定一个积分方程解的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.

Fixed point theorems for generalized \((\alpha ,\psi )\)-contraction mappings in rectangular quasi b-metric spaces

Abstract