Fixed Point Theorems for Multi-valued α-Fcontractions in Partial metric spaces with Some Application

Abstract

This paper aims to prove a fixed point theorem for multi-valued mapping using α-F-contraction in partial metric spaces. Furthermore, we prove a fixed point theorem 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, Sgroi and Vetro and Kumar. We also provided illustrative examples and some applications to integral equations.

Keywords

• fixed point
• multi-valued mapping
• α -f-contraction
• hardy-rogers contraction
• partial metric spaces
• integral equation