V. P. Motornyi, O. V. Motornaya, “On the best $L_1$-approximation by algebraic polynomials to truncated powers and to classes of functions with $L_1$-bounded derivative”, Izv. RAN. Ser. Mat., 1999, Volume 63, Issue 3,Pages 147

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On the best $L_1$-approximation by algebraic polynomials to truncated powers and to classes of functions with $L_1$-bounded derivative

V. P. Motornyi, O. V. Motornaya

Dnepropetrovsk State University

Abstract: We establish the asymptotic behaviour of the best $L_1$-approximations of the kernels $(x-a)_+^{r-1}$, $r>2$ and the corresponding classes $W_1^r$ by algebraic polynomials.

MSC: 41A50, 41A10

Received: 06.05.1997

DOI: 10.4213/im246