• 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$_X$.

• 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?

• 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 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.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.91-99
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• 2010

In this paper we introduce the concept of asymptotically almost negatively associated random variables in a Hilbert space and obtain the strong law of large numbers for a strictly stationary asymptotically almost negatively associated sequence of H-valued random variables with zero means and finite second moments. As an application we prove a strong law of large numbers for a linear process generated by asymptotically almost negatively random variables in a Hilbert space with this result.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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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.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.43-51
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• 1995

In this paper, we introduce the almost linear spaces, a generalization of linear spaces. We prove that if the almost linear space X has a finite basis then, as in the case of a linear space, the cardinality of bases for the almost linear space X is unique. In the case X = Wx ＋ Vx, we prove that B'= {$\chi$'$_1,...,x'_n} is a basis for the algebraic dual X$^#$ of X if B = {$\chi$'$_1,...,x'_n} is a basis for the almost linear space X. And we have an example X($\neq$Wx ＋ Vx) which has no such a basis.

• 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.

• 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 applied mathematics & informatics
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• v.4 no.2
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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.