• 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.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.867-877
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• 2024

The objective of this article is to acquire analogs for the degree of best one-sided approximation to investigate some Jackson's well-known theorems for best one-sided approximations in weighted L_p,α-spaces. In addition, some operators that are used to approximate unbounded functions have been introduced as be algebraic polynomials in the same weighted spaces. Our main results are given in terms of degree of the best one-sided approximation in terms of averaged modulus of smoothness.