Fixed-point theorems in extended fuzzy metric spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive mappings

Abstract

In this article we would like to present a new type of fuzzy contractive mappings which are called $\alpha-\phi-\mathcal{M}^{0}$ fuzzy contractive and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive, and then we demonstrate two theorems which ensure the existence of a fixed point for these two types of mappings. And so we combine and generalize some existing notions in the literature ([5], [7]). Proved these theorems in the extended fuzzy metric spaces are in the more general version than the existing in the literature ones.