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  1. Topology and Dynamics
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  5. 2026

Topological Methods in Algebra and Analysis

Icon: calendar TMAA Session #2.2 | 2026 Jul 14 from 11:00AM to 11:25AM (Zagreb) | B3-69

Subevent of TMAA Session #2

‟Negation functions in fuzzy metric spaces: topological aspects and fixed point results” by Alba Baeza-Bosca; Valentín Gregori; Juan-José Miñana

Abstract:

The theory of fuzzy metric spaces, originating from the foundational work of Kramosil and Michalek, continues to be an active and relevant area of research. From a topological perspective, these spaces have been extensively investigated, while fixed point theory within this framework remains a topic of ongoing interest.

A recent contribution has explored the incorporation of negation functions as a tool to develop a more general setting in fuzzy metric spaces. In particular, such functions have been proposed both to define alternative topological structures and to extend existing fixed point results.

In this talk, we examine the role of negation functions from these two viewpoints. Our analysis shows that whenever an alternative way of deriving a topology can be obtained through negation functions, it coincides with the classical topology introduced by George and Veeramani. Furthermore, when negation functions are assumed to be strict or strong, the resulting classes of fuzzy contractions do not provide genuine extensions of previously known ones. Consequently, the fixed point results obtained in this context can be regarded as direct corollaries of earlier theorems.