Non-Expansive Multi-Valued Mappings and Convexity in Fuzzy Metric Space

Abstract

In this article, we delve into the concept of convexity within fuzzy metric spaces and delve into their structural characteristics. We present several theorems concerning the existence of coincidence points in fuzzy convex metric spaces. Furthermore, we introduce the notion of star-shaped subsets within fuzzy convex metric spaces. Within these star-shaped subsets, we showcase various fixed point theorems for mappings of the non-expansive type that commute. In the final section, we expand the definition of fuzzy convex metric spaces and provide a significant example of such a space. Additionally, we uncover specific fixed point theorems applicable to multi-valued mappings that are non-expansive.

Keywords

• pm-spaces
• fixed point
• coincidence points
• non-expansive mappings
• convex structure