Quasi (s,r)-Contractive Multi-Valued Operators and Related Fixed Point Theorems

Ei Ei Nyein,Dianlu Tian,Aung Khaing Zaw

doi:10.3390/math8010064

Abstract

This paper gives the new concepts of quasi ( s , r ) -contractive multi-valued operators and establishes some related fixed point results for such operators. In addition, an application to certain functional equations arising from dynamic programming is given to illustrate the usage of the obtained results.

Highlights

Introduction and PreliminariesAs it is well known to all, the proverbial Banach contraction mapping principle is a very useful, simple and classical tool in modern mathematics, and has been widely used in many branches of mathematics and physics
Many mathematicians have researched and generalized the Banach contraction mapping principle along different directions, such as the fixed point theorem of fuzzy metric spaces, C ∗ -algebra valued metric spaces and so on [1,2,3,4,5]
The complete metric space is replaced by different types of metric spaces [6,7,8]

Summary

Introduction

Introduction and PreliminariesAs it is well known to all, the proverbial Banach contraction mapping principle is a very useful, simple and classical tool in modern mathematics, and has been widely used in many branches of mathematics and physics. In 1969, Nadler [10] and Reich [11,12] introduced the fixed point theorems of the multi-valued contractive operators respectively. [13] Let ( X, d) be a metric space and T : X → CB( X ) be a multi-valued operator.

Results

Conclusion