Some results on convergences in fuzzy metric spaces and fuzzy normed spaces
Commun. Korean Math. Soc. 2020 Vol. 35, No. 1, 185-199
https://doi.org/10.4134/CKMS.c180460
Published online January 31, 2020
Kyugeun Cho, Chongsung Lee
Myong Ji University; Inha University
Abstract : In this paper, we introduce the definitions of $s_p$-convergent sequence in fuzzy metric spaces and fuzzy normed spaces. We investigate relations of convergence, $s_p$-convergence, $s_{\infty}$-convergence and $st$-convergence in fuzzy metric spaces and fuzzy normed spaces. We also study $s_p$-convergence, $s_{\infty}$-convergence and $st$-convergence using the subsequence of convergent sequence in fuzzy metric spaces and fuzzy normed spaces. Stationary fuzzy normed spaces are defined and investigated. We finally define $s_p$-closed sets, $s_{\infty}$-closed sets and $st$-closed sets in fuzzy metric spaces and fuzzy normed spaces and investigate relations of them.
Keywords : Fuzzy metric space, fuzzy normed space, $s_p$-convergence, $s_{\infty}$-convergence, $st$-convergence, $s_p$-closed sets
MSC numbers : 54A40
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