Nonlinear Analysis: Theory, Methods & Applications
Multivalued generalized nonlinear contractive maps and fixed points
Section snippets
Introduction and preliminaries
Let be a metric space, a collection of nonempty subsets of , and a collection of nonempty closed bounded subsets of a collection of nonempty closed subsets of a collection of nonempty compact subsets of .
For any , let where . is called the Hausdorff metric induced by .
An element is called a fixed point of a multivalued map if . We denote . A sequence in
The results
First we prove a fixed point result which improves the recent fixed point result [5, Theorem 2.1] of Ciric. Theorem 2.1 Let be a complete metric space with a -distance . Let be a multivalued map. Assume that the following conditions hold: there exist a constant and a function such that for each the map , defined by is lower semicontinuous for any , there exists satisfyingand
Acknowledgements
The authors would like to thank the referees for their valuable comments and suggestions which led to an improved presentation of the manuscript.
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