Fixed points of (α,β,F∗) and (α,β,F∗∗)-weak Geraghty contractions with an application

Abstract

This study aims to provide new classes of (α,β,F∗)-weak Geraghty contraction and (α,β,F∗∗)-weak Geraghty contraction, a self generalized contractions on any metric space. Further we find that the mappings satisfying the definition of such contractions have unique fixed point if the base space is complete. Also there is an application for existing unique solution of two-point boundary value problem.