Abstract
AbstractIn this work, we define the concept of G-monotone nonexpansive multivalued mappings defined on a metric space with a graph G. Then we obtain sufficient conditions for the existence of fixed points for such mappings in hyperbolic metric spaces. This is the first kind of such results in this direction.
Highlights
1 Introduction Fixed point theorems for monotone single-valued mappings in a metric space endowed with a partial ordering have been widely investigated
Investigation of the existence of fixed points for single-valued mappings in partially ordered metric spaces was initially considered by Ran and Reurings in [ ] who proved the following result
3 Main results We begin with the following well-known theorem, which gives the existence of a fixed point for monotone single-valued and multivalued contraction mappings in metric spaces endowed with a graph
Summary
1 Introduction Fixed point theorems for monotone single-valued mappings in a metric space endowed with a partial ordering have been widely investigated. Generalizing the Banach contraction principle for multivalued mapping to metric spaces, Nadler [ ] obtained the following result. Investigation of the existence of fixed points for single-valued mappings in partially ordered metric spaces was initially considered by Ran and Reurings in [ ] who proved the following result.
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