Coconvex approximation of periodic functions
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Abstract
The Jackson inequality \(E_n (f) \leqslant c\omega _3 \left( {f,\frac{\pi }{n}} \right)\) relates the value of the best uniform approximation E n (f) of a continuous 2π-periodic function f: ℝ → ℝ by trigonometric polynomials of degree ≤ n − 1 to its third modulus of continuity ω 3(f, t). In the present paper, we show that this inequality is true if continuous 2π-periodic functions that change their convexity on [−π, π) only at every point of a fixed finite set consisting of an even number of points are approximated by polynomials coconvex to them.
Keywords
Periodic Function Trigonometric Polynomial Algebraic Polynomial Jackson Inequality Convex Upward
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