Fixed points of an F-contraction on metric spaces with a graph

Abstract

We introduce a new type of contraction on a metric space endowed with a graph and prove fixed point theorems that generalize some of the results related with G-contraction for a directed graph G. Examples are given to justify that our contractions are more general than many others in this area.

Keywords:

• fixed point
• Picard operator
• F–G-contraction
• G-contraction
• F-contraction
• connected graph

2010 AMS Subject Classifications:

• Primary: 47H10
• Secondary: 05C40
• 54H25