Fixed point theorems for β-contraction mapping in Smyth complete quasi-metric spaces

Abstract

In this article, we begin by recalling the concept of quasi-metric spaces, providing all the important definitions, and explaining the different types of completeness. Following this foundational overview, we introduce a new type of contraction called the β-contraction. We then prove the existence and uniqueness of fixed points for such contractions in Smyth’s complete quasi-metric spaces. To illustrate our results, we present a relevant example. Finally, we conclude by generalizing the last theorem to a broader context, demonstrating the robustness and applicability of our findings.