Date of Publication :3rd July 2024

Abstract: This paper explores standard fixed-point theorems in various metric spaces, including complete, compact, and generalised metric spaces. The aim is to understand the conditions under which these theorems hold and to present some generalisations and applications. Specifically, we examine the fixed-point theorems in traditional, a-metric, and partial metric spaces, providing detailed proofs and discussions on their implications. We analyse the relationships between different types of fixed-point theorems and how they can be applied in various fields, such as computer science, economics, and engineering. Through this comprehensive study, we aim to contribute to understanding fixed point theory and its practical utility in solving real-world problems.

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