A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations

Fangfang Yan,Yongfu Su,Qiansheng Feng

doi:10.1186/1687-1812-2012-152

Fangfang Yan, Yongfu Su + Show 1 more

Open Access

https://doi.org/10.1186/1687-1812-2012-152

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Abstract

Abstract The aim of this paper is to extend the results of Harjani and Sadarangani and some other authors and to prove a new fixed point theorem of a contraction mapping in a complete metric space endowed with a partial order by using altering distance functions. Our theorem can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence of a solution for a periodic boundary value problem.

Highlights

The Banach contraction principle is a classical and powerful tool in nonlinear analysis
In [ – ], the authors prove some types of weak contractions in complete metric spaces respectively
Harjani and Sadarangani proved some fixed point theorems for weak contraction and generalized contractions in partially ordered metric spaces by using the altering distance function in [, ] respectively

Summary

Introduction

The Banach contraction principle is a classical and powerful tool in nonlinear analysis. The existence of a fixed point for weak contraction and generalized contractions was extended to partially ordered metric spaces in [ , – ].

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Conclusion