Partial B-metric Spaces Research Articles

α−ψ−φ -contractive mappings in ordered partial b-metric spaces

α−ψ−φ -contractive mappings in ordered partial b-metric spaces

Some common fixed point results in ordered partial b-metric spaces

Abstract In this paper, we introduce a modified version of ordered partial b-metric spaces. We demonstrate a fundamental lemma for the convergence of sequences in such spaces. Using this lemma, we prove some fixed point and common fixed point results for ( ψ , φ ) -weakly contractive mappings in the setup of ordered partial b-metric spaces. Finally, examples are presented to verify the effectiveness and applicability of our main results. MSC: 47H10, 54H25.

Partial b-Metric Spaces and Fixed Point Theorems

The purpose of this paper is to introduce the concept of partial b-metric spaces as a generalization of partial metric and b-metric spaces. An analog to Banach contraction principle, as well as a Kannan type fixed point result is proved in such spaces. Some examples are given which illustrate the results.