Let f{hook} be a function in Lp(T), 1 ≤ p < +∞, or le f{hook} be a continuous function on the torus T if p = + ∞, and let Kn be the nth Fejér kernel. We prove that, although the sequence {∥f{hook} - Kn*f{hook}∥p} is not monotone in general, it still has a monotonicity property. Namely, if m < n, then ∥f{hook} - Kn*f{hook}∥p ≤ (2 + m n)| 2 p - 1|∥f{hook} - Km *f{hook}∥p. © 1989.
Colzani, L. (1989). Is the approximation of a function by its Fejér means monotone?. JOURNAL OF APPROXIMATION THEORY, 56(2), 152-154 [10.1016/0021-9045(89)90106-8].
Is the approximation of a function by its Fejér means monotone?
COLZANI, LEONARDO
1989
Abstract
Let f{hook} be a function in Lp(T), 1 ≤ p < +∞, or le f{hook} be a continuous function on the torus T if p = + ∞, and let Kn be the nth Fejér kernel. We prove that, although the sequence {∥f{hook} - Kn*f{hook}∥p} is not monotone in general, it still has a monotonicity property. Namely, if m < n, then ∥f{hook} - Kn*f{hook}∥p ≤ (2 + m n)| 2 p - 1|∥f{hook} - Km *f{hook}∥p. © 1989.File in questo prodotto:
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