Fixed point results for $\alpha_s$-nonexpensive mappings on partial $b$-metric spaces

Pakeeta Sukprasert, Muhammad Nazam, Muhammad Arshad, Khanitin Muangchoo-in

Abstract

In this paper, we introduce the class of $\alpha_s$-non-expansive mappings which satisfy a generalized contractive condition. We establish some fixed point theorems for a introduced mappings in a complete partial $b$-metric space. Our results generalize some fixed point results existing in the current literature. We give an example which explains the main result. As an application, we show the existence of the solution of a boundary valued problem.