Fixed point existence results of F-Kannan type contraction on a metric space with directed graph

Abstract

In this article, we have attained some interesting results on existence of fixed points for a newly developed larger class of self mappings called FG -Kannan defined on a metric space equipped with a special type of graph called ʊ-orbitally connected graph. This extended class is a merger of the most recently developed Kannan type mapping called F-Kannan contractions defined in a metric space and G-Kannan mapping defined in a metric space with an underlying graph. It is highlighted through example that such a graph condition is sufficient to study fixed points of FG -Kannan mappings. Several interesting examples are illustrated which justify that our obtained results are more general and further, many previously developed fixed point results related to Kannan mappings are encompassed in our main result. The article closes by raising some open problems of this work.