Fixed point of interpolative contraction on metric space endowed with graph

Abstract

In this manuscript, a new concept of interpolative contraction, namely interpolative Kannan type (G-α-µ)-contraction is introduced in metric space endowed with a graph and novel condi tions for which the new mapping is a Picard operator are investigated. The preeminence of this type of contraction is that it complements and subsumes a few corresponding notions in the literature. Substantial examples are constructed to validate the assumptions of our obtained results and to show their distinction from the existing ones.