• 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$_X$.

• 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.

• 충청수학회지
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• 제13권1호
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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?

• 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.

• 충청수학회지
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• 제15권1호
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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.

• 대한수학회보
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• 제34권1호
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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)$.

• 대한수학회논문집
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• 제10권4호
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• pp.855-866
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• 1995

We prove that if a nals X is reflexive, then $X = W_X + V_X$. We prove also that if an als X has a finite basis, then $X = W_X + V_X$ if and only if X is reflexive.

• 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 $x{\;}{\in}{\;}X$.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.573-581
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• 1997

In this paper we prove a weak common fixed point theo-rem in a normed almost linear space which is different from the result of S. P. Singh and B.A. Meade [9]. However for a Banach X our theorem is equal to the result of S. P. Singh and B. A. Meade.

• 대한수학회논문집
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• 제12권2호
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• pp.211-219
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• 1997

In [6] we proved that if a nals X is reflexive, then $X = W_X + V_X$ . In this paper we show that, for a split nals $X = W_X + V_X$, X is reflecxive if and only if $V_X$ and $W_X$ are reflcxive.