On the generalizations of Kalandia’s Lemma

Abstract

Based on Bernstein’s Theorem, Kalandia’s Lemma describes the error estimate and the smoothness of the remainder under the second part of Holder norm when a Holder function is approximated by its best polynomial approximation. In this paper, Kalandia’s Lemma is generalized to the cases that the best polynomial is replaced by one of its four kinds of Chebyshev polynomial expansions, the error estimates of the remainder are given out under Holder norm or the weighted Holder norms.