Common Fuzzy Fixed Point Theorems for Fuzzy \(F\)-Weak Contractions in Non-Archimedean Fuzzy Metric Spaces

In this paper, we extend the concept of fuzzy \(F\)-weak contractions to the framework of non-Archimedean fuzzy metric spaces in the sense of George and Veeramani \cite{George}. A generalized class of fuzzy \(F\)-weak contractions for nonlinear mappings of arbitrary finite arity is introduced. Under suitable conditions, we establish several common fuzzy fixed point theorems for pairs of mappings in this setting. The obtained results generalize and unify various existing fixed point theorems in fuzzy metric spaces and related structures. An illustrative example is provided to demonstrate the applicability of the main results.