Generalized Suzuki Type $\mathcal Z$-Contraction in Complete Metric Spaces

A. Padcharoen, P. Kumam, P. Saipara, P. Chaipunya

In this paper, we introduce the notion of Suzuki type $\mathcal{Z}$-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.