A Fixed Point Theorem and Generalized Non-Archimedean Quasi-Ordered Metric Spaces and Its Applications

Abstract

In this paper, we introduce the concepts of quasi-orders which are generalization of partial orders and the concepts of a generalized non-Archimedean quasi-ordered metric space which are generalization of non-Archimedean metric spaces. And we investigate the generalized non-Archimedean quasi-ordered metric on the set of all mappings from a non-Archimedean normed space to a complete non-Archimedean normed space. Further, we prove a fixed point theorem for a contraction in d-complete metric spaces. As an application, we give the stability for some functional equations.