On estimates for the moduli of smoothness of functions with a transformed Fourier series.

Tikhonov, Sergej Yu.

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Displaying similar documents to “On estimates for the moduli of smoothness of functions with a transformed Fourier series.”

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Let E be a real normed linear space with unit ball B and unit sphere S. The classical modulus of convexity of J. A. Clarkson [2] δ_E(ε) = inf {1 - 1/2||x + y||: x,y ∈ B, ||x - y|| ≥ ε} (0 ≤ ε ≤ 2) is well known and it is at the origin of a great number of moduli defined by several authors. Among them, D. F. Cudia [3] defined the directional, weak and directional weak modulus of convexity of E, respectively, as δ_E...