F-Contractive multivalued maps and coincidence points

Marwan A Kutbi

doi:10.1186/1029-242x-2013-141

Abstract

In this paper, we prove a result on the existence of an f -orbit for generalized f -contractive multivalued maps. Then, we establish main results on the existence of coincidence points and common fixed points for generalized f -contractive maps not involving the extended Hausdorff metric and the continuity condition. Our results either generalize or improve a number of metric fixed point results. MSC: 47H10; 47H09; 54H25

Highlights

Using the concept of Hausdorff metric, Nadler [ ] established the following fixed point result for multivalued contraction maps, which in turn is a generalization of the wellknown Banach contraction principle
First we establish a lemma with respect to a w-distance, which is an improved version of the lemma given in [ ], and we prove a key lemma on the existence of an f -orbit for generalized f -contractive maps
Since the sequence {f} is in the complete metric space X satisfying the inequality ( ), it follows from Lemma . that {f} converges in X

Summary

Introduction

Using the concept of Hausdorff metric, Nadler [ ] established the following fixed point result for multivalued contraction maps, which in turn is a generalization of the wellknown Banach contraction principle. [ ] Let (X, d) be a complete metric space, and let T : X → CB(X) be a contraction map.

Results

Conclusion