Abstract
AbstractLet $\rho\in\Re$ ρ ∈ ℜ (the class of all nonzero regular function modulars defined on a nonempty set Ω) and G be a directed graph defined on a subset C of $L_{\rho}$ L ρ . In this paper, we discuss the existence of fixed points of monotone G-contraction and G-nonexpansive mappings in modular function spaces. These results are the modular version of Jachymski fixed point results for mappings defined in a metric space endowed 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 aim of this paper is to give the correct extension by studying the existence of fixed points for multivalued mappings in modular function spaces endowed with a graph G
3 Main results We begin with the following theorem that gives the existence of a fixed point for monotone multivalued mappings in modular spaces endowed with a graph
Summary
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. Different authors considered the problem of existence of a fixed point for contraction mappings in partially ordered sets; see [ – ] and the references cited therein.
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