Year: 2017
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 1 : pp. 74–92
Abstract
Suppose that a continuous 2π-periodic function f on the real axis changes its monotonicity at points yi:−π≤y2s<y2s−1<⋯<y1<π, s∈N. In this paper, for each n≥N, a trigonometric polynomial Pn of order cn is found such that: Pn has the same monotonicity as f, everywhere except, perhaps, the small intervals(yi−π/n,yi+π/n)and‖where N is a constant depending only on \min\limits_{i=1,\cdots,2s}\{y_i-y_{i+1}\},\ c,\ c(s) are constants depending only on s,\ \omega_3(f,\cdot) is the modulus of smoothness of the 3-rd order of the function f, and \|\cdot\| is the max-norm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2017.v33.n1.7
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 1 : pp. 74–92
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Periodic functions comonotone approximation trigonometric polynomials Jackson-type estimates.
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