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
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.
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