• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.475-484
• /
• 2005

The main aim of this paper is to consider the fuzzy norm, define the fuzzy Banach spaces, its quotients and prove some theoremes and in particular Open mapping and Closed graph theoremes on these spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.2
• /
• pp.281-286
• /
• 2009

In this paper, we introduce the notion of the complete fuzzy norm on a linear space. And we consider some relations between the fuzzy completeness and ordinary completeness on a linear space.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.597-606
• /
• 2009

In this paper, we introduce the notion of the statistically complete fuzzy norm on a linear space. And we consider some relations between the fuzzy statistical completeness and ordinary completeness on a linear space.

• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.547-559
• /
• 2021

We first define the notions of filter continuous, filter sequentially continuous and filter strongly continuous in the framework of fuzzy normed space (FNS), and then we introduce the notion of filter slowly oscillating sequences in the setting of FNS and shows that this notion is stronger than slowly oscillating sequences. Further, we define the concept of filter slowly oscillating continuous functions, filter Cesàro slowly oscillating sequences as well as some other related notions in the aforementioned space and investigate several related results.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.5 no.2
• /
• pp.175-178
• /
• 2005

In the present paper, we observe a relation between fuzzy norms and induced crisp norms on a linear space. We first prove that if $\rho_1,\;\rho_2$ are equivalent fuzzy norms on a linear space, then for every $\varepsilon\in(0.1)$, the induced crisp norms $P_\varepsilon^1,\;and\;P_\varepsilon^2$, respectively are equivalent. Since the converse does not hold, we prove it under some strict conditions. And consider the following theorem proved in [8]: Let $\rho$ be a lower semicontinuous fuzzy norm on a normed linear space X, and have the bounded support. Then $\rho$ is equivalent to the fuzzy norm $\chi_B$ where B is the closed unit ball of X. The lower semi-continuity of $\rho$ is an essential condition which guarantees the continuity of $P_\varepsilon$, where 0 < e < 1. As the last result, we prove that : if $\rho$ is a fuzzy norm on a finite dimensional vector space, then $\rho$ is equivalent to $\chi_B$ if and only if the support of $\rho$ is bounded.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.707-721
• /
• 2013

In this paper, we investigate a fuzzy version of stability theory for the following functional equation f(x+y)+f(x-y)-2f(x)-f(y)-f(-y)=0 in the sense of M. Mirmostafaee and M. S. Moslehian.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.4 no.2
• /
• pp.9-12
• /
• 1994

Let X, Y be normed linear spaces, and let p$_{1}$, p.sub 2/ be lower semi-continuous fuzzy norms on X, Y respectively, and have the bounded supports on X, Y respectively. In this paper, we prove that if Y is conplete, the set of all fuzzy continuous linear maps from X into Y is a fuzzy complete fuzzy normed linear space.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.3
• /
• pp.453-464
• /
• 2016

In this paper, we investigate the solution of the following functional inequality $$N(f(x)+f(y)+f(z),t){\geq}N(f(x+y+z),mt)$$ for some fixed real number m with $\frac{1}{3}$ < m ${\leq}$ 1 and using the fixed point method, we prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.

• East Asian mathematical journal
• /
• v.30 no.3
• /
• pp.271-281
• /
• 2014

In this paper, we consider the following cubic functional equation f(3x + y) + f(3x - y) = f(x + 2y) + 2f(x - y) + 2f(3x) - 3f(x) - 6f(y) and prove the generalized Hyers-Ulam stability for it in fuzzy normed spaces.

• Communications of the Korean Mathematical Society
• /
• v.31 no.4
• /
• pp.729-743
• /
• 2016

In the current work, the intuitionistic fuzzy version of Hyers-Ulam stability for a nonic functional equation by applying a fixed point method is investigated. This way shows that some fixed points of a suitable operator can be a nonic mapping.