• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.705-710
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• 2010

Let $C_1(X)$ be a normed linear space over ${\mathbb{R}}^m$, and S be an n-dimensional subspace of $C_1(X)$ with spaned by {$s_1,{\cdots},s_n$}. For each ${\ell}$- tuple vectors F in $C_1(X)$, the two-sided best simultaneous approximation problem is $$\min_{s{\in}S}\;\max\limits_{i=1}^\ell\{{\parallel}f_i-s{\parallel}_1\}$$. A $s{\in}S$ attaining the above minimum is called a two-sided best simultaneous approximation or a Chebyshev center for $F=\{f_1,{\cdots},f_{\ell}\}$ from S. This paper is concerned with algorithm for calculating two-sided best simultaneous approximation, in the case of continuous functions.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.141-148
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• 2009

We consider various algorithms calculating best onesided simultaneous approximations. We assume that X is a compact subset of $\mathbb{R}^{m}$ satisfying $X=\overline{intX}$, S is an n-dimensional subspace of C(X), and $\mu$ is any 'admissible' measure on X. For any l-tuple $f_1,\;{\cdots},\;f_{\ell}$ in C(X), we present various ideas for best approximation to F from S(F). The problem of best (both one and two-sided) approximation is a linear programming problem.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.127-140
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• 1998

In this paper, we discuss the characterizations and uniqueness of a one-sided best simultaneous approximation for a compact subset from a convex subset of a finite-dimensional subspace of a normed linear space $C_1(X)$. The motivation is furnished by the characterizations of the one-sided best simultaneous approximations for a finite subset ${f_1, \ldots, f_\ell}$ for any $\ell \in N$.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.435-442
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• 2010

This paper is concerned with algorithm for calculating one-sided best simultaneous approximation, in the case of continuous functions. we will apply any subgradient algorithm. In other words, we consider the algotithms from a mathematical, rather then computational, point of view.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.435-444
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• 1996

Let X be a normed linear space and K be a nonempty subset of X.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.155-167
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• 1996

Let X be a compact Hausdorff space, C(X) denote the set of all continuous real valued functions on X and $\ell \in N$ be any natural number.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.367-376
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• 1996

We characterize best simultaneous approximations from a finite-dimensional subspace of a normed linear space. In the characterization we reveal usefulness of a minimax theorem presented in [2,4].

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.193-204
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• 1996

Let U and V be nonempty compact subsets of two Hausdorff topological vector spaces. Suppose that a function $J : U \times V \to R$ is such that for each $\upsilon \in V, J(\cdot, \upsilon)$ is lower semi-continuous and convex on U, and for each $ u \in U, J(u, \cdot)$ is upper semi-continuous and concave on V.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.669-674
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• 2022

In this paper, we shall consider some properties of the metric projection as a set valued mapping. For a set G in a metric space E, the mapping 𝜋_G; x → 𝜋_G(x) of E into 2^G is called set valued metric projection of E onto G. We investigated the properties related to the projection P_S(·)(·) and 𝜋_S(·)(·) as one-sided best simultaneous approximations.