New Existence of Fixed Point Results in Generalized Pseudodistance Functions with Its Application to Differential Equations

Sujitra Sanhan,Winate Sanhan,Chirasak Mongkolkeha

doi:10.3390/math6120324

Abstract

The purpose of this article is to prove some existences of fixed point theorems for generalized F -contraction mapping in metric spaces by using the concept of generalized pseudodistance. In addition, we give some examples to illustrate our main results. As the application, the existence of the solution of the second order differential equation is given.

Highlights

In recent years, several generalizations of standard metric spaces have appeared in connection with generalizing a Banach contraction theorem
In 1996, Kada, Suzuki and Takahashi [1] defined the notions of a w-distance which is a generalized metric and provided a generalized Caristi’s fixed point theorem
Let ( X, d) be a metric space equipped with a generalized pseudodistance J [14]

Summary

Introduction

Several generalizations of standard metric spaces have appeared in connection with generalizing a Banach contraction theorem. In 1996, Kada, Suzuki and Takahashi [1] defined the notions of a w-distance which is a generalized metric and provided a generalized Caristi’s fixed point theorem. In 2013, by using the concept of Meir–Keeler, Suzuki, Ćirić, Achymski, and Matkowski mappings, the fixed point results in uniform spaces were given [4]. Mongkolkeha and Kumam [5] used the notion of generalized weak contraction to prove the existence results of fixed point in b-metric spaces. Established a new contraction called F-contraction and acquired a fixed point result which generalized a Banach contraction in many ways. By using the notion of F-contraction, we prove some new existence theorems of fixed points in generalized pseudodistances. We establish the existence solution of a second order differential equation by using our fixed point results

Preliminaries

F-Contraction Mapping

Main Results

Applications