Nearly Comonotone Approximation of Periodic Functions

被引：0

作者：

G.A.Dzyubenko ^{[1
]}

机构：

[1] Yu. A.Mitropolsky International Mathematical Center of NASU

来源：

Analysis in Theory and Applications | 2017年 / 33卷 / 01期

关键词：

Periodic functions; comonotone approximation; trigonometric polynomials; Jacksontype estimates;

D O I：

暂无

中图分类号：

O174.41 [逼近论];

学科分类号：

070104 ;

摘要：

Suppose that a continuous 27r-periodic function f on the real axis changes its monotonicity at points y;:-π≤ y;<y;<… < y;<π,s ∈ IN.In this PaPer,for each n≥N,a trigonometric polynomial P;of order cn is found such that:P;has the same monotonicity as f,everywhere except,perhaps,the small intervals（y;-π/n,y;+π/n）and‖f-P;‖<c（s）ω;（f,π/n）,where N is a constant depending only on mini=1,...,2s {y;-y;},c,c（s） are constants depending only on s,ω;（f;,·） is the modulus of smoothness of the 3-rd order of the function f,and ||·|| is the max-norm.

引用

页码：74 / 92

页数：19