Fixed Point Theorems and Applications in Fuzzy Quasi-Metric Spaces

Abstract

This paper delves into the realm of fuzzy quasi-metric spaces, emphasizing the identification of fixed points for specific mappings within this unique framework. We have formulated fixed-point theorems designed for various mapping types in these spaces, underscoring their practical relevance and applicability. Moreover, we have uncovered principles akin to Kransnoselski's theorems, specifically tailored to fuzzy quasi-metric spaces. Our research further investigates the stability of fixed points under certain conditions, providing a comprehensive analysis of their behavior. To elucidate our findings, we have incorporated illustrative examples, which serve to clarify and exemplify the theoretical concepts discussed. This inclusion of examples not only enhances understanding but also demonstrates the practical implementation of our theorems. Through our work, we aim to contribute significantly to the recent advancements in the study of fuzzy quasi-metric spaces and fixed-point theory. Our findings offer valuable insights and extend the current knowledge base, paving the way for future research and applications in this evolving field. Ultimately, our paper stands as a testament to the ongoing progress and innovation in fuzzy quasi-metric space theory, reflecting its growing importance and potential for further exploration.