Fixed point results for nonlinear contractions with application to integral equations

Abstract

We present a number of fixed and common fixed point theorems for a class of nonlinear contractions in metric spaces and metric spaces endowed with graphs. Our results complement, extend and generalize a number of fixed point theorems including a recent fixed point theorem of Kim et al. [Suzuki-type of common fixed theorem in metric spaces, J. Nonlinear Convex Anal. 16 (2015) 1779–1786]. We also discuss an application to a system of integral equations.