Coupled fixed point theorems in $C^{*}$-algebra-valued b-metric spaces with application

Chuanzhi Bai

doi:10.1186/s13663-016-0560-1

Abstract

AbstractBased on the concept of a $C^{*}$ C ∗ -algebra-valued b-metric space, this paper establishes some coupled fixed point theorems for mapping satisfying different contractive conditions on such space. As applications, we obtain the existence and uniqueness of a solution for an integral equation.

Highlights

Introduction and preliminariesIn, Bakhtin [ ] introduced b-metric space as a generalization of metric space
Ma and Jiang [ ] initially introduced the concept of a C∗-algebra-valued b-metric space which generalized the concept of b-metric spaces, and they established certain basic fixed point theorems for self-map with contractive condition in this new setting
Cao [ ] first studied some coupled fixed point theorems in the context of complete C∗-algebra-valued metric spaces

Summary

Introduction

Introduction and preliminariesIn , Bakhtin [ ] introduced b-metric space as a generalization of metric space. Ma and Jiang [ ] initially introduced the concept of a C∗-algebra-valued b-metric space which generalized the concept of b-metric spaces, and they established certain basic fixed point theorems for self-map with contractive condition in this new setting. Many researchers investigated coupled fixed point theorems in ordered metric spaces and have given some applications [ – ]. Cao [ ] first studied some coupled fixed point theorems in the context of complete C∗-algebra-valued metric spaces.

Results

Conclusion