Abstract:
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.