Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2020; 35(1): 185-199

Online first article August 27, 2019      Printed January 31, 2020

https://doi.org/10.4134/CKMS.c180460

Copyright © The Korean Mathematical Society.

Some results on convergences in fuzzy metric spaces and fuzzy normed spaces

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