A note on approximate fixed point property and Du-Karapinar-Shahzad’s intersection theorems

Wei-Shih Du

doi:10.1186/1029-242x-2013-506

Abstract

In this note, we give new short proofs of Du-Karapinar-Shahzad’s intersection theorems for multivalued non-self-maps in complete metric spaces. MSC:47H10, 54H25.

Highlights

Introduction and preliminariesLet us begin with some basic definitions and notations that will be needed in this paper
Du, Karapinar and Shahzad [ ] established the following intersection existence theorem of coincidence points and fixed points of multivalued non-self-maps of Kannan type and Chatterjea type
We present an existence theorem for p-approximate fixed point property and approximate fixed point property, which is a somewhat generalized form of [, Theorem . ] and is one of the key technical devices in the new short proofs of Theorems . and

Summary

Introduction

Introduction and preliminariesLet us begin with some basic definitions and notations that will be needed in this paper. We give new short proofs of Du-Karapinar-Shahzad’s intersection theorems for multivalued non-self-maps in complete metric spaces. Du, Karapinar and Shahzad [ ] established the following intersection existence theorem of coincidence points and fixed points of multivalued non-self-maps of Kannan type and Chatterjea type.

Results

Conclusion