Existence of fixed point results in orthogonal extended b-metric spaces with application

Abstract

In this paper, we investigate the conditions for the existence of fixed-point for generalized contractions in the orthogonal extended b-metric spaces endowed with an arbitrary binary relation. We establish some unique fixed-point theorems. The obtained results generalize and improve many earlier fixed point results. We also provide some nontrivial examples to corroborate our results. As an application, we investigate solution for the system of boundary value problem.

Keywords

• extended b-metric
• orthogonal metric
• fixed point
• unique fixed point