• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.177-182
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• 2018

The purpose of this paper is to present approximation of $C_0-sequentially$ equicontinuous semigroups on a sequentially complete locally convex space X.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.47-51
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• 2019

The purpose of this paper is to present approximation of $C_0$-sequentially equicontinuous semigroups on a sequentially complete locally convex space X.

• East Asian mathematical journal
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• v.6 no.1
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• pp.111-121
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• 1990

Let E be a locally convex Hausdorff space and let $\Gamma$ be a calibration for E. In this note we proved that if E is sequentially complete and a multi-vaiued operaturA in E is $\Gamma$-accretive such that $D(A){\subset}Re$ (I+$\lambda$A) for all sufficiently small positive $\lambda$, then A generates a nonlinear $\Gamma$-contraction semiproup {T(t) ; t>0}. We also proved that if E is complete, $Gamma$ is a dually uniformly convex calibration, and an operator A is m-$\Gamma$-accretive, then the initial value problem $$\{{\frac{d}{dt}u(t)+Au(t)\;\ni\;0,\;t >0,\atop u(0)=x}\.$$ has a solution $u:[0,\infty){\rightarrow}E$ given by $u(t)=T(t)x={lim}\limit_{n\rightarrow\infty}(I+\frac{t}{n}A)^{-n}x$ each $x{\varepsilon}D(A)$.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.331-339
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• 1998

We show a series of improved subseries convergence results, e.g., in a sequentially complete locally convex space X every weakly $c_0$-Cauchy series on X must be $c_0$-convergent. Thus, if X contains no copy of $c_0$, then every weakly $c_0$-Cauchy series on X must be subseries convergent.