Sharp inequalities for convolution-type operators
Abstract
Let μ be a probability measure on [- a, a], a > 0, and let x0ε{lunate}[- a, a], f ε{lunate} Cn([-2a, 2a]), n ≥ 0 even. Using moment methods we derive best upper bounds to |∫-aa ( [f(x0 + y) + f(x0 - y)] 2) μ(dy) - f(x0)|, leading to sharp inequalities that are attainable and involve the second modulus of continuity of f(n) or an upper bound of it. © 1989.
Publication Title
Journal of Approximation Theory
Recommended Citation
Anastassiou, G. (1989). Sharp inequalities for convolution-type operators. Journal of Approximation Theory, 58 (3), 259-266. https://doi.org/10.1016/0021-9045(89)90027-0
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