Upper bounds of best one-sided approximations of the classes $W^rL_\psi$ in the metric of $L$

V. G. Doronin^a, A. A. Ligun<sup>b

a</sup> Dnepropetrovsk State University
^b Dneprodzerzhinsk Industrial Institute

Abstract: The lowest upper bound is obtained for best one-sided approximations of classes $W^rL_\psi$ ($r=1,2,\dots$) by trigonometric polynomials and splines of minimum deficiency with equidistant knots, in the metric of space $L$, where $W^rL_\psi=\{f:f(x+2\pi)=f(x)$, $f^{(r-1)}(x)$ is absolutely continuous, $\|f^{(r)}\|_{L_\psi}\le1\}$ and $L_\psi$ is an Orlicz space.

UDC: 517.5

Received: 30.12.1975

 English version: Mathematical Notes, 1977, 22:2, 633–640

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