Fixed point results for single and multivalued mappings with application in graph theory

Abstract

Let (X, D) be a complete metric space and H, F be single and multivalued mappings on X respectively. In this paper, we investigate two new types of fixed point theorems from a set of single and multivalued mappings in a complete metric spaces 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.

Subject Classification:

• 05C20
• 47H09
• 47H10

Keywords:

• Fixed point
• Single and multi-valued mapping
• G-contraction
• Directed graph