Fixed Points for ψ -Graphic Contractions with Application to Integral Equations

Abstract

The aim of this paper is to define modified weak $\alpha$-$\psi$-contractive mappings and to establish fixed point results for such mappings defined on partial metric spaces using the notion of triangular $\alpha$-admissibility. As an application, we prove new fixed point results for graphic weak $\psi$-contractive mappings. Moreover, some examples and an application to integral equation are given here to illustrate the usability of the obtained results.