Common Fixed Points of Two Mappings regarding a Generalizedc-Distance over a Banach Algebra

Ladan Aryanpour,Hamidreza Rahimi,Ghasem Soleimani Rad,Huseyin Isik

doi:10.1155/2021/6623606

Abstract

In this article, applying the concept of a generalizedc-distance in coneb-metric spaces over Banach algebra with a nonnormal solid cone therein, we establish several common fixed point theorems for two noncontinuous mappings satisfying the Han-Xu-type contraction. Our results are interesting, since they are not equivalent to former well-known results regarding awt-distance inb-metric spaces while they contain recent results corresponding to a generalizedc-distance in coneb-metric spaces.

Highlights

Introduction and PreliminariesIn 2015, Bao et al [1] suggested a generalized c-distance, which extended many former definitions in [2,3,4,5,6,7,8,9,10]) and references therein
In this article, applying the concept of a generalized c-distance in cone b-metric spaces over Banach algebra with a nonnormal solid cone therein, we establish several common fixed point theorems for two noncontinuous mappings satisfying the Han-Xu-type contraction
In 2018, Han and Xu [19] proved some common fixed point results by removing the assumption of continuity of the mappings and by deleting the hypothesis of the normality of the cone

Summary

Introduction

Introduction and PreliminariesIn 2015, Bao et al [1] suggested a generalized c-distance, which extended many former definitions in [2,3,4,5,6,7,8,9,10]) and references therein. In this article, applying the concept of a generalized c-distance in cone b-metric spaces over Banach algebra with a nonnormal solid cone therein, we establish several common fixed point theorems for two noncontinuous mappings satisfying the Han-Xu-type contraction. In 2015, Huang et al [18] proposed a c-distance in cone metric spaces over a Banach algebra E.

Results

Conclusion