Some Common Fixed Point Results for Generalized $alpha_*$-$psi$-contractive Multi-valued Mappings on Ordered Metric Spaces with Application to Initial Value Problem

Abstract

In 2012, Samet, et al. introduced the notion of $alpha$-$psi$-contractive type mappings. They have been establish some fixed point theorems for the mappings on complete metricspaces. In this paper, we introduce the notion of generalized $alpha_*$-$psi$-contractive multi-valued mappings and we give some related fixed point results on ordered metric spaces via  application to an initial value problem.