Fixed point of set-valued graph contractive mappings

Abstract

Let (X, d) be a metric space and let F, H be two set-valued mappings on X. We obtained sufficient conditions for the existence of a common fixed point of the mappings F, H in the metric space X endowed with a graph G such that the set of vertices of G, V(G) = X and the set of edges of G, E(G) ⊆ X × X. MSC: Primary 47H10; secondary 47H04; 47H07; 54C60; 54H25

Common Fixed Points of Weakly Commuting Multivalued Mappings on a Domain of Sets Endowed with Directed Graph

“…The aim of this paper is to prove some coincidence point and common fixed point results for discontinuous multivalued graphic ψ-contractive mappings defined on the family of closed and bounded subsets of a metric space endowed with a graph G. These results extend and strengthen various comparable results in the existing literature [1,9,12,19,20,23] .…”

“…(3) If E(G) := X × X, then clearly G is connected and our Corollary 2.5 improves and generalizes Theorem 2.1 in [9], Theorem 3.2 in [23] and Theorem 3.1 in [19].…”

“…For fixed point result of mappings defined on ε−chainable metric space, we refer to [9] and references mentioned therein.…”

“…Beg and Butt [9] proved the existence of fixed points of multivalued mapping in metric spaces endowed with a graph G. Recently, Abbas et al, [1] obtained fixed points of set valued mappings satisfying certain graphic contraction conditions with set valued domain endowed with a graph. Nicolae et al [25] established some fixed points of multivalued generalized contractions in metric spaces endowed with a graph.…”

Common Fixed Points of Generalized α-ψ-contractive Type Selfmappings and Multivalued Mappings

“…In 2010, Rouhani and Moradi [3] proved the following common fixed point result for multi-valued mappings. point results for multivalued mappings defined on a metric space endowed with a graph [4]. In this paper combining ideas of the above mentioned literature we give some new results on common fixed points of α-ψ-contractive self-mappings and multivalued mappings [5][6][7][8].…”