Mina Dinarvand - Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box ۱۶۳۱۵-۱۶۱۸, Tehran, Iran

In this paper, we introduce the notions of fuzzy \alpha-Geraghty contraction type mapping and fuzzy \beta-\varphi-contractive mapping and establish some interesting results on the existence and uniqueness of fixed points for these two types of mappings in the setting of fuzzy metric spaces and non-Archimedean fuzzy metric spaces. The main results of our work generalize and extend some known comparable results in the literature. Furthermore, several illustrative examples are given to support the usability of our obtained results.

Fixed point, Fuzzy alpha-Geraghty contraction type mapping, Fuzzy beta-varphi-contractive mapping, Fuzzy metric space, Non-Archimedean fuzzy metric space