Generalized Suzuki type Z-contraction in complete metric spaces

Abstract

In this paper, we introduce the notion of Suzuki type Z-contraction and study the corresponding fixed point property. This kind of contraction generalizes the Banach contraction and unifies several known type of nonlinear contractions. We consider a nonlinear operator satisfying a nonlinear contraction in a metric space and prove fixed point results. As an application, we apply our result to show the solvability of nonlinear Hammerstein integral equations.