^{}Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran

Abstract

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.

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