Theorem on Fixed Points in Fuzzy 3-Metric Space - Subashini, Nagamani; Priyadharshini, Aisu (Optimality, 2026)
Our study examines fixed point theory within the context of fuzzy 3-metric spaces, which are a logical extension of traditional fuzzy metric spaces that take three-variable relationships into account. In contrast to the conventional Banach-type or Ćirić-type conditions that have been previously examined in the literature, our main contribution is the introduction of a novel generalized contractive condition.In this new contractive framework, we prove the existence and uniqueness of fixed points on fuzzy 3-metric spaces, and construct a fixed point theorem. The scope of fixed point results in generalized fuzzy settings is expanded by this development, which also makes them more applicable to systems with complex interactions and multi-way uncertainty. To illustrate the usefulness of our result, examples are provided.