Fixed point results for a new $ \alpha $-$ \theta $-Geraghty type contraction mapping in metric-like space via $ \mathcal{C}_\mathcal{G} $-simulation functions

Abstract

This paper aims to introduce the new concept of an $ \alpha $-$ \theta $-Geraghty type contraction mapping using $ \mathcal{C}_{\mathcal{G}} $-simulation in a metric-like space. Additionally, through this type of contraction, we establish fixed point results that generalize several known fixed point results in the literature. We provide some examples as an application that proves the credibility of our results.

Keywords

• metric-like space
• fixed point
• geraghty contraction
• ($ \alpha
• \theta $)-admissible mapping
• $ \mathcal{c}_{\mathcal{g}} $-simulation function