Geodesic
On the Jackson--Stechkin inequality for algebraic polynomials
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 246-253

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The Jackson–Stechkin inequality is considered, which estimates the value of the best uniform approximation of a continuous function by algebraic polynomials on a closed interval in terms of values of the modulus of continuity of the approximated function. A variant of the inequality with second-order modulus of continuity and explicit specification of the argument of the modulus of continuity and the constant is proved.
Keywords: Jackson inequality, approximation by algebraic polynomials, modulus of continuity. 
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A. V. Mironenko. On the Jackson--Stechkin inequality for algebraic polynomials. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 246-253. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a22/