Equivalence between various Shape Preserving Approximations of periodic functions

D. Leviatan; O.V. Motorna; I.O. Shevchuk

doi:10.15421/242518

Equivalence between various Shape Preserving Approximations of periodic functions

D. Leviatan (Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University), https://orcid.org/0000-0003-0180-5065
O.V. Motorna (Taras Shevchenko National University of Kyiv), https://orcid.org/0009-0003-4963-3239
I.O. Shevchuk (Taras Shevchenko National University of Kyiv), https://orcid.org/0000-0003-1140-373X

Abstract

We show that the validity of Jackson-type estimates in comonotone and coconvex approximations of continuous $$$2\pi$$$-periodic functions by trigonometric polynomials is equivalent to the validity of the corresponding estimates of approximation by continuous $$$2\pi$$$-periodic piecewise algebraic polynomials with equidistant knots, having a minor additional property.

Keywords

shape preserving approximation; trigonometric polynomial; Jackson; comonotone; coconvex; piecewise polynomial

MSC 2020

Pri 42A05, Sec 42A10, 41A17, 41A25, 41A29

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