Existence fixed-point theorems in the partial b-metric spaces and an application to the boundary value problem

Abstract

In this paper, we prove some results on the Hausdorff partial b-metrics. We prove some new Lemmas regarding convergence of the sequences in the Hausdorff partial b-metric spaces. The obtained results generalize and improve many existing fixed-point results. The examples are given for the explanation of theory. The existence of the solution to the boundary value problem is proved via fixed-point approach.

Keywords

• fixed point
• multivalued almost contractions
• partial b-metric space
• application