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On approximation by families of linear polynomial operators in $l_P$-spaces, $0<p<1$

K. V. Runovskii

T. H. Shevchenko Chernihiv State Pedagogical Institute

Abstract: New applications are given for a method of approximation by families of linear polynomial operators in $L_p$-spaces with $0<p<1$ that was developed by the author in previous papers. In particular, a direct theorem and an inverse theorem on approximation 'by angle' of trigonometric polynomials are proved in the case of higher-order moduli of smoothness.

UDC: 517.51

MSC: Primary 41A10, 41A27, 41A63, 42A10; Secondary 41A50, 42B99

Received: 27.09.1993

 English version: Russian Academy of Sciences. Sbornik. Mathematics, 1995, 82:2, 441–459

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