Common Coupled Fixed Point Theorems on C ⋆ -Algebra-Valued Partial Metric Spaces

Gunaseelan Mani,Arul Joseph Gnanaprakasam,Precious B Khumalo,Yaé U Gaba

doi:10.1155/2022/3336095

Abstract

In this paper, we prove common coupled fixed point theorems on complete C ⋆ -algebra-valued partial metric spaces. An example and application to support our result are presented.

Highlights

In 1987, Guo and Lakshmikantham [1] introduced the concept of a coupled fixed point
We prove common coupled fixed point theorems on complete C⋆-algebra-valued partial metric spaces
In 2006, Bhaskar and Lakshmikantham [2] introduced the concept of a mixed monotone property for the first time and investigated some coupled fixed point theorems for mappings

Summary

Introduction

In 1987, Guo and Lakshmikantham [1] introduced the concept of a coupled fixed point. In 2006, Bhaskar and Lakshmikantham [2] introduced the concept of a mixed monotone property for the first time and investigated some coupled fixed point theorems for mappings. In 2014, Ma et al [22] introduced the notion of a C⋆ -algebra-valued metric space and proved fixed point theorem. In 2015, Batul and Kamran [23] proved fixed theorems on C⋆ -algebra-valued metric space. In 2016, Alsulami et al [24] proved fixed point theorems on C∗-algebra-valued metric space. In 2016, Cao and Xin [25] proved common coupled fixed point theorems in C∗-algebra-valued metric spaces. In 2011, Aydi et al [30] proved coupled fixed point theorems on ordered partial metric space. In 2019, Chandok et al [44] proved fixed point theorems on C∗-algebra-valued partial metric space. We prove common coupled fixed point theorems on C∗-algebra-valued partial metric space

Preliminaries

Main Results

Application

Conclusion