A New Contraction with an Application for Integral Equations

Abstract

In this study, we introduce a new definition called δ-contraction. However, we prove some theorems for mappings satisfying the δ-contraction and touch upon fixed points. In the obtained theorems, we also show the existence and uniqueness of fixed points. In order to prove the validity of the results of our main theorems, we give a few examples as well as an application that reveals the solution of some integral equations.

Keywords

• <i>δ</i>-contraction
• fractional integral equation
• fixed point