Abstract
AbstractWe give a generalization of the Banach contraction principle on a modular metric space endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as the modular metric version of Jachymski’s fixed point result for mappings on a metric space with a graph.
Highlights
1 Introduction Fixed point theorems for monotone single-valued mappings in a metric space endowed with a partial ordering have been widely investigated
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
The aim of this paper is to discuss the existence of fixed points for single Lipschitzian mappings defined on some subsets of modular metric spaces X endowed with a graph G
Summary
Fixed point theorems for monotone single-valued mappings in a metric space endowed with a partial ordering have been widely investigated. 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. Different authors considered the problem of existence of a fixed point for contraction mappings in partially ordered sets; see [ – ] and references cited therein.
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