On metrization of fuzzy metrics and application to fixed point theory

Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems

“…In addition, since M(x n(k) , x n(k)+1 , c) is an e-sequence we can find k 0 ∈ N such that M(x n(k) , x n(k)+1 , c) ≫ e − δ for every k ≥ k 0 . So, on account of inequality (9) we have, for every k ≥ k 0 , the following:…”

“…Nonetheless, fuzzy metrics show some differences compared with classical ones which still make their study of interest nowadays. On the one hand, they differ in some purely metric topics as completeness or fixed point theory, which are two active topics of research in the literature (see, for instance, the following recent references [5][6][7][8][9][10][11]). On the other hand, fuzzy metrics have been successfully used, compared with their classical counterparts, in engineering problems such as model estimation, modelling multi-agent systems or image filtering (see, for instance, [12][13][14][15][16][17] and references therein).…”