Jackson's type estimate of nearly coconvex approximation
German Dzyubenko

TL;DR
This paper develops a Jackson-type estimate for nearly coconvex approximation of periodic functions, providing a method to construct trigonometric polynomials that closely approximate the function while preserving convexity properties except near specified points.
Contribution
The paper introduces a new Jackson-type estimate for nearly coconvex approximation, extending classical results to functions with changing convexity points and providing explicit bounds.
Findings
Constructs trigonometric polynomials matching convexity except near specified points.
Provides approximation bounds involving the modulus of continuity of order 4.
Establishes dependence of approximation quality on the spacing of convexity change points.
Abstract
Suppose that a continuous on the real axis -periodic function changes its convexity at points on each period: and for the rest the points are defined periodically. In the paper, for each a trigonometric polynomial of order is found such that: has the same convexity as everywhere except, perhaps, the small neighborhoods of the and where is a constant depending only on and are constants depending only on is the modulus of continuity of the -th order of the function and is the max-norm.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Mathematical Approximation and Integration · Advanced Harmonic Analysis Research
