• 대한수학회지
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• 제42권1호
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• pp.129-134
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• 2005

Lpt X be a reduced Stein space and L a holomorphic line bundle on X. L is spanned by its global sections and the associated holomorphic map $h_L\;:\;X{\to}P(H^0(X, L)^{\ast})$ is an embedding. Choose any locally convex vector topology ${\tau}\;on\;H^0(X, L)^{\ast}$ stronger than the weak-topology. Here we prove that $h_L(X)$ is sequentially closed in $P(H^0(X, L)^{\ast})$ and arithmetically Cohen -Macaulay. i.e. for all integers $k{\ge}1$ the restriction map ${\rho}_k\;:\;H^0(P(H^0(X, L)^{\ast}),\;O_{P(H^0(X, L)^{\ast})}(k)){\to}H^0(h_L(X),O_{hL_(X)}(k)){\cong}H^0(X, L^{\otimes{k}})$ is surjective.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.859-866
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• 1999

In Eucliden k-space the cone of vectors x=($\chi$1, $\chi$2, ...,$\chi$k) satisfying $\chi$1$\leq$$\chi$ 2, $\leq$...$\leq$$\chi$k and {{{{ SUM { }`_{j } ^{k } }}= 1 $\chi$j=0 is generated by the vectors vj=(j-k,...j-k...j) having j-k's in its first j coordinates and j's for the remaining k-j coordinates for 1$\leq$j$\leq$i

• 대한수학회지
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• 제40권1호
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• pp.29-40
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• 2003

Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : KlongrightarrowK be a strictly hemi-contractive operator. Under some conditions we obtain that the Mann iteration method with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. The results presented in this paper generalize the corresponding results in [l]-[7], [20] and others.

• 대한수학회지
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• 제45권2호
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• pp.377-392
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• 2008

Let X be a real reflexive Banach space with a uniformly $G\hat{a}teaux$ differentiable norm, C a nonempty closed convex subset of X, T : C $\rightarrow$ X a continuous pseudocontractive mapping, and A : C $\rightarrow$ C a continuous strongly pseudocontractive mapping. We show the existence of a path ${x_t}$ satisfying $x_t=tAx_t+(1- t)Tx_t$, t $\in$ (0,1) and prove that ${x_t}$ converges strongly to a fixed point of T, which solves the variational inequality involving the mapping A. As an application, we give strong convergence of the path ${x_t}$ defined by $x_t=tAx_t+(1-t)(2I-T)x_t$ to a fixed point of firmly pseudocontractive mapping T.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.437-442
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• 2021

In this paper, we study the characterizations of two-sided best simultaneous approximations for ℓ-tuple subset from a closed convex subset of ℝ^m with ℓ^m₁(w)-norm. Main fact is, k^* is a two-sided best simultaneous approximation to F from K if and only if there exist f₁, …, f_p in F, for any k ∈ K $${\mid}{\sum\limits_{i=1}^{m}}sgn(f_{ji}-k^*_i)k_iw_i{\mid}{\leq}\;{\sum\limits_{i{\in}Z(f_j-k^*)}}\;{\mid}k_i{\mid}w_i$$ for each j = 1, …, p and 𝐰 ∈ W.

• 대한수학회보
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• 제34권1호
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• pp.93-102
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• 1997

Let C be a nonempty closed convex subset of a Banach space E and let $T_1, \cdots, T_N$ be nonexpansive mappings from C into itself (recall that a mapping $T : C \longrightarrow C$ is nonexpansive if $\left\$\mid$ Tx - Ty \right\$\mid$ \leq \left\$\mid$ x - y \right\$\mid$$ for all $x, y \in C$). We consider the fixed point problem for nonexpansive mappings : find a common fixed point, i.e., find a point in $\cap_{i=1}^N Fix(T_i)$, where $Fix(T_i) := {x \in C : x = T_i x}$ denotes the set of fixed points of $T_i$.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.701-712
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• 2009

In this paper, we first introduce a family S = {$S_n$ : C ${\rightarrow}$ C} of non-Lipschitzian mappings, called total asymptotically nonexpansive (briefly, TAN) on a nonempty closed convex subset C of a real Banach space X, and next give necessary and sufficient conditions for strong convergence of the sequence {$x_n$} defined recursively by the algorithm $x_{n+1}$ = $S_nx_n$, $n{\geq}1$, starting from an initial guess $x_1{\in}C$, to a common fixed point for such a continuous TAN family S in Banach spaces. Finally, some applications to a finite family of TAN self mappings are also added.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제3권2호
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• pp.187-193
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• 2003

In this paper, a systematic design method of the intelligent PAM fuzzy controller for nonlinear systems using the efficient tools-Linear Matrix Inequality and the intelligent digital redesign is proposed. In order to digitally control the nonlinear systems, the TS fuzzy model is used for fuzzy modeling of the given nonlinear system. The convex representation technique also can be utilized for obtaining TS fuzzy models. First, the analog fuzzy-model-based controller is designed such that the closed-loop system is globally asymptotically stable in the sense of Lyapunov stability criterion. The simulation results strongly convince us that the proposed method has great potential in the application to the industry.

• 대한수학회보
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• 제37권4호
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• pp.743-753
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• 2000

In the space $C_1(X)$ of real-valued continuous functions with $L_1-norm$, every bounded set has a relative Chebyshev center in a finite-dimensional subspace S. Moreover, the set function $F\rightarrowZ_S(F)$ corresponding to F the set of its relative Chebyshev centers, in continuous on the space B[$C_1(X)$(X)] of nonempty bounded subsets of $C_1(X)$ (X) with the Hausdorff metric. In particular, every bounded set has a relative Chebyshev center in the closed convex set S(F) of S and the set function $F\rightarrowZ_S(F)$(F) is continuous on B[$C_1(X)$ (X)] with a condition that the sets S(.) are equal.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.673-678
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• 2008

Let $W_{\alpha}$, be a recursively generated quadratically hyponormal weighted shift with a weight sequence ${\alpha}$ : 1, (1, $\sqrt{x}$, $\sqrt{y}$)$^{\wedge}$. In [4] Curto-Jung showed that R = {(x,y) : $W_{1,\;(1,\;{\sqrt{x}},\;{\sqrt{y}})^{\wedge}}$ is quadratically hyponormal} is a closed convex with nonempty interior, which guarantees that there are a lot of quadratically hyponormal weighted shifts with first two equal weights. They suggested a problem computing expressions of certain extremal points of R. In this note we obtain a partial answer of their extremal problem.