Exploring Fuzzy Triple Controlled Metric Spaces: Applications in Integral Equations

Abstract

In this article, we delve into the study of fuzzy triple controlled metric spaces, investigating their properties and presenting a range of illustrative examples. We emphasize the broader applicability of this concept in comparison to fuzzy rectangular metric spaces and fuzzy rectangular b-metric spaces. By introducing the novel concept of (α-ψ)-fuzzy contractive mappings, we derive fixed point results specifically designed for complete fuzzy triple controlled metric spaces. Our theorems extend and enrich previous findings in this field. Additionally, we demonstrate the practical significance of our study by applying our findings to the solution of an integral equation and providing an example of its application. Furthermore, we propose potential avenues for future research endeavors.

Keywords

• fixed point
• fuzzy rectangular metric space
• controlled fuzzy metric space
• α-admissible mapping
• (α-ψ)-contraction
• fuzzy triple controlled metric space