Some results on 3-normed spaces and fuzzy 3-normed spaces

Abstract

In this paper we give some definitions and basic concepts related with 3-normed space like we give definitions of closed subset, closure subset, bounded subset and equivalent norms. Moreover, we prove every Cauchy sequence in 3-normed space is bounded and a Cauchy sequence is convergent in an 3-normed space if and only if it has a convergent subsequence. Thereafter, we generalize this facts to fuzzy 3-normed space