• Journal of applied mathematics & informatics
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• v.5 no.2
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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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• v.11 no.1_2
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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$_X$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.79-85
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• 2000

In this paper, we have an affirmative solution of G. Godini's open question ([3]): If a normed almost linear space Y is complete, is the normed almost linear space B(X, (Y,C)) complete?

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.21 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.115-125
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• 1997

In [3,4,5], G. Godini introduced a normed almost linear space(nals), generalizing the concept of a normed linear space. In contrast with the case of a normed linear space, tha norm of a nals $(X, $\mid$$\mid$$\mid$ \cdot $\mid$$\mid$$\mid$)$ does not generate a metric on X $(for x \in X \backslash V_X we have $\mid$$\mid$$\mid$ x - x $\mid$$\mid$$\mid$ \neq 0)$.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.35-41
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• 2002

In this paper, we prove the stability of a Jensen's functional equation on a normed almost linear space.