• 충청수학회지
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• 제19권2호
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• pp.197-206
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• 2006

In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated. We introduce quasi-2-normed spaces and quasi-(2; p)-normed spaces, and investigate the properties of quasi-2-normed spaces and quasi-(2; p)-normed spaces.

• 충청수학회지
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• 제26권4호
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• pp.915-922
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• 2013

In this paper, we investigate some properties of 2-norm midpoints and 2-normed equalities in 2-normed spaces.

• 호남수학학술지
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• 제43권3호
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• pp.417-431
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• 2021

In this study, we introduced the notions of rough statistical convergence and defined the set of rough statistical limit points of a sequence and obtained statistical convergence criteria associated with this set in 2-normed space. Then, we proved that this set is closed and convex in 2-normed space. Also, we examined the relations between the set of statistical cluster points and the set of rough statistical limit points of a sequence in 2-normed space.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.517-523
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• 1998

In this paper we prove that a normed almost linear space \hat{X} can be embedded in a normed linear space X when a normed almost linear space X has a basis and splits as X=V+W. Also we have a metric induced by a norm on a normed almost linear space as a corollary.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.365-371
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• 2003

In this paper, we introduce metrics d, p and ${\mu}$ on a normed almost linear space (X, III.III). And we prove that above three metrics are equivalent if a normed almost linear space X has a basis and splits as X = W$_X$ + V$_X$.

• 한국지능시스템학회논문지
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• 제18권2호
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• pp.268-271
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• 2008

In this paper, we introduce the notions of a fuzzy convergence of sequences, fuzzy Cauchy sequence and the related fuzzy completeness on a fuzzy normed linear space. And we investigate some properties relative to fuzzy normed linear spaces. In particular, we prove an equivalent conditions that a fuzzy norm defined on a ordinary normed linear space is fuzzy complete.

• 대한수학회보
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• 제21권1호
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• pp.1-5
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• 1984

The notion of linear 2-normed spaces was introduced by S. Gahler ([8,9,10,11]), and these space have been extensively studied by C. Diminnie, R. Ehret, S. Gahler, K. Iseki, A. White, Jr, and others. For nonzero vectors x,y in X, let V(x,y) denote the subspace of X generated by x and y. A linear 2-normed space (X,v) is said to be strictly convex ([3]) if v(x+y,z)=v(x,z)+v(y+z) and z not.mem.V(x,y) imply that y=ax for some a>0. Some characterizations of strict convexity for linear 2-normed spaces are given in [1,3,4,5,12]. Also, a linear 2-normed space (X,v) is said to be strictly 2-convex ([6]) if v(x,y)=v(x,z)=v(y,z)=1/3v(x+z, y+z)=1 implies that z=x+y. These space have been studied in [2,4,6,13]. It is easy to see that every strictly convex linear 2-normed space is always strictly 2-convex but the converse is not necessarily true. Throughout this paper, let (X,v) denote a linear 2-normed space.

• 대한수학회보
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• 제36권2호
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• pp.379-388
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• 1999

In this paper, we introduce a semi-metric on a normed almost linear space X via functional. And we prove that a normed almost linear space X is complete if and only if $V_X$ and $W_X$ are complete when X splits as X=$W_X$ + $V_X$. Also, we prove that the dual space $X^\ast$ of a normed almost linear space X is complete.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권3호
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• pp.185-192
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• 2003

It is shown that every almost linear mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a linen. mapping when h(rx) = rh(x) (r > 0,$r\;{\neq}\;1$$x{\;}{\in}{\;}X$, that every almost quadratic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a quadratic mapping when $h(rx){\;}={\;}r^2h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$, and that every almost cubic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a cubic mapping when $h(rx){\;}={\;}r^3h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$.

• 대한수학회보
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• 제44권2호
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• pp.291-308
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• 2007

The motivation of this paper is to present a new and interesting notion of intuitionistic fuzzy n-normed linear space. Cauchy sequence and convergent sequence in intuitionistic fuzzy n-normed linear space are introduced and we provide some results onit. Furthermore we introduce generalized cartesian product of the intuitionistic fuzzy n-normed linear space and establish some of its properties.