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 some results on convergences in fuzzy metric spaces and fuzzy normed spaces Commun. Korean Math. Soc.Published online August 27, 2019 Kyugeun Cho and 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, $s$-convergence, $s_p$-convergence, $s_{\infty}$-convergence, $st$-convergence, $s_p$-closed sets MSC numbers : 54A40 Full-Text :