Fixed point theorems for generalized α−η−ψ−Geraghty contraction type mappings in α − η −complete metric spaces

In this paper, we introduce the concept of generalized α − η − ψ − Geraghty contraction type mappings and prove the unique fixed point theorems for such mappings in α − η − complete metric spaces without assuming the subadditivity of ψ . We also give an example for supporting the result and present an application using our main result to obtain a solution of the integral equation.