Some Fixed Point Theorems for Boyd and Wong Type Contraction Mapping in Ordered Partial Metric Spaces with an Application

Santosh Kumar,Faustine Nziku,Chi Ming Chen

doi:10.1155/2022/7591420

Abstract

This paper establishes and proves a fixed point theorem for Boyd and Wong type contraction in ordered partial metric spaces. In doing so, we have extended several existing results into ordered complete partial metric spaces. An illustrative example is given to demonstrate the validity of our results. Finally, the existence of the solution of nonlinear integral equation is discussed as an application of the main result.

Highlights

Introduction and PreliminariesBanach’s fixed point theorem [1] has been extensively studied to solve the problems in nonlinear analysis since many years. is theorem provides the existence and uniqueness of the solution
In 1969, Boyd and Wong [2] gave an important generalization of the Banach fixed point theorem by the application of control function in the Banach contraction condition
Kumar [10] established and proved a fixed point theorem for Boyd and Wong type contraction for a pair of maps in complete metric spaces

Summary

Introduction

Introduction and PreliminariesBanach’s fixed point theorem [1] has been extensively studied to solve the problems in nonlinear analysis since many years. is theorem provides the existence and uniqueness of the solution. If (M, ρ) is a complete metric space and T: M ⟶ M is a self-contractive mapping, T has a unique fixed point u ∈ M. Kumar [10] established and proved a fixed point theorem for Boyd and Wong type contraction for a pair of maps in complete metric spaces.

Results

Conclusion