Fixed Point Theorems for Multi-valued $\alpha$-$F$- contractions in Partial metric spaces with an Application

Abstract

This paper aims to prove a fixed point theorem for multi-valued mapping using $\alpha-F$-contraction in partial metric spaces. Furthermore, a fixed point theorem is proved for F-Hardy-Roger’s multi-valued mappings in ordered partial metric spaces. Specifically, this paper intends to generalize the theorems by Ali and Kamran [3], Sgroi and Vetro [32] and Kumar [15]. We also provided illustrative examples and an application to integral equations.