Fixed Point and Endpoint Theorems for $(\alpha,\beta)$-Meir-Keeler Contraction on the Partial Hausdorff Metric

Komi Afassinou, Ojen Kumar Narain

Abstract

The purpose of this work is to introduce the notion of a multi-value strictly $(\alpha,\beta)$-admissible mappings and a multi-value $(\alpha,\beta)$-Meir-Keeler contraction with respect to the partial Hausdorff metric $\mathcal{H}_{p}$ in the framework of partial metric spaces. In addition, we present fixed points and endpoints results for a multi-valued $(\alpha,\beta)$-Meir-Keeler contraction mappings in the framework of the complete partial metric spaces. The results obtained in this work provides extension as well as substantial generalizations and improvements of several well-known results on fixed point theory and its applications.