Approximation of continuous periodic functions by de la Vallee Poussin sums
Ie.Yu. Ovsii, A. S. Serdyuk
TL;DR
This paper provides an estimate for how closely de la Vallee Poussin sums approximate continuous periodic functions, using the modulus of continuity, and shows this estimate is optimal.
Contribution
It introduces a precise deviation estimate for de la Vallee Poussin sums based on the modulus of continuity, demonstrating its optimality.
Findings
The deviation estimate is expressed in terms of the modulus of continuity.
The established estimate cannot be improved using the Lebesgue inequality analogue.
The results apply to continuous periodic functions and provide bounds for approximation quality.
Abstract
We obtain an estimate of the deviation of de la Vallee Poussin sums V_{n,n/2}(f;x) from continuous functions f, expressed in terms of values of theirs modulus of continuity. It is established that this estimate can't be improved by using the well-known analogue of the Lebesgue inequality for de la Vallee Poussin sums
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Mathematical Approximation and Integration · Mathematical functions and polynomials