Coconvex approximation of periodic functions

被引：0

作者：

Zalizko V.D. ^{[1
]}

机构：

[1] National Pedagogic University, Kyiv

来源：

Ukrainian Mathematical Journal | 2007年 / 59卷 / 1期

关键词：

Periodic Function; Trigonometric Polynomial; Algebraic Polynomial; Jackson Inequality; Convex Upward;

D O I：

10.1007/s11253-007-0003-6

中图分类号：

学科分类号：

摘要：

The Jackson inequality En(f) ≤ comega3 ({f,π/n) relates the value of the best uniform approximation En (f) of a continuous 2π-periodic function f: ℝ → ℝ by trigonometric polynomials of degree ≥ n-1 to its third modulus of continuity ω 3(f, t). In the present paper, we show that this inequality is true if continuous 2π-periodic functions that change their convexity on [-π, π) only at every point of a fixed finite set consisting of an even number of points are approximated by polynomials coconvex to them. © Springer Science+Business Media, Inc. 2007.

引用

页码：28 / 44

页数：16

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