New Generalizations of Set Valued Interpolative Hardy-Rogers Type Contractions in b-Metric Spaces

Muhammad Usman Ali,Monairah Alansari,Hassen Aydi,Tuncer Acar

doi:10.1155/2021/6641342

Abstract

Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contraction mappings on b-metric spaces and proved that on a complete b-metric space, whose all closed and bounded subsets are compact, the set valued interpolative Hardy-Rogers type contraction mapping has a fixed point. This article presents generalizations of above results by omitting the assumption that all closed and bounded subsets are compact.

Highlights

There are numerous studies on interpolation inequalities in literature
Various interpolation properties find their applications in computer science and have many deep purely logical consequences
Gogatishvili and Koskela [5] presented variant interpolation properties of Besov spaces defined on metric spaces

Summary

Introduction

There are numerous studies on interpolation inequalities in literature. In 1999, Chua [1] gave some weighted Sobolev interpolation inequalities on product spaces. Karapinar et al [10] gave the interpolative HardyRogers type contraction as follows: a mapping K : ðW, dWÞ → ðW, dWÞ is called an interpolative Hardy-Rogers type contraction if dW Kwa, Kwb This article presents two new generalizations of set valued interpolative Hardy-Rogers type contraction mappings. We ensure the existence of fixed points of such maps on a complete b-metric space without considering the assumption that all closed and bounded subsets must be compact.

Results

Conclusion