Approximation and existence of fixed points via interpolative enriched contractions

Abstract

In this paper, we define interpolative enriched contractions of Kannan type, Hardy-Rogers type and Matkowski type, by enriching existing interpolative contractions, in the setting of convex metric space. For these newly introduced contractions, we prove existence of fixed points and approximation results using Krasnoselskij iteration. Examples are also given to indicate the relevance of our results in comparison to some of the existing ones in the literature.