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Keywords:
fuzzy metric space; asymptotic fuzzy $\psi $-contractive mapping; asymptotic fuzzy Meir–Keeler mapping; fixed point
fuzzy metric space; asymptotic fuzzy $\psi $-contractive mapping; asymptotic fuzzy Meir–Keeler mapping; fixed point
Summary:
Fixed point theory in fuzzy metric spaces has grown to become an intensive field of research. However, due to the complexity involved in the nature of fuzzy metrics, the authors need to develop innovative machinery to establish new fixed point theorems in such kind of spaces. In this paper, we propose the concepts of asymptotic fuzzy $\psi$-contractive and asymptotic fuzzy Meir-Keeler mappings, and describe some new machinery by which the corresponding fixed point theorems are proved. In this sense, the techniques used for the proofs in Section 5 are completely new.
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