Ordered Non-Archimedean Fuzzy Metric Spaces and Some Fixed Point Results

After the definition of the concept of fuzzy metric space by some authors 1–3 , the fixed point theory on these spaces has been developing see, e.g., 4–9 . Generally, this theory on fuzzy metric space is done for contractive or contractive-type mappings see 2, 10–13 and references therein . In this paper we introduce the concept of fuzzy order ψ-contractive mappings and give two fixed point theorems on ordered non-Archimedean fuzzy metric spaces for fuzzy order ψ-contractive type mappings. Then, using an idea in 14 , we will provide a common fixed point theorem for weakly increasing single-valued mappings in a complete fuzzy metric space endowed with a partial order induced by an appropriate function. Some fixed point results on ordered probabilistic metric spaces can be found in 15 . For the sake of completeness, we briefly recall some notions from the theory of fuzzy metric spaces used in this paper.