Fixed Point Theorems for New Type of Mappings in Metric Spaces and Application

Abstract

In this article, we introduce a new notion of   η‐contraction and prove Widdle fixed point theorems, which provide a new generalization of the Banach contraction principle in different way than in the known results from the existing literature. Further, we include examples in support of our results. Finally, an application is presented which shows the existence and uniqueness of a solution for a class of Volterra type integral equations of the second kind.