Fixed Point Results in Modular b-Metric-like Spaces with an Application

Abstract

In this study, we introduce a new space called the modular b-metric-like space. We investigate some properties of this new concept and define notions of ξ-convergence, ξ-Cauchy sequence, ξ-completeness and ξ-contraction. The existence and uniqueness of fixed points in the modular b-metric-like space are handled. Moreover, we give some examples and an application to an integral equation to illustrate the usability of the obtained results.

Keywords

• modular b-metric-like space
• fixed point
• contraction principle
• integral equation