Abstract
Let WrH w be the subclass of those functions of Cr[a, b], for which ω(f (r),δ)⩽ω(δ), where ω(δ) is a given modulus of continuity, and Pn be the space of algebraic polynomials of degree at most n and πn(f) be the polynomial of best approximation for f(x) on [a, b]. Estimates for and moduli of continuity of the operators of best approximation on WrH w are established. For example, if ω(δ)=δα, then
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