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Lipschitz classes and convolution approximation processes

Published online by Cambridge University Press:  24 October 2008

Z. Ditzian
Z. Ditzian
Affiliation:
University of Alberta, Edmonton
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Extract

For a continuous function f(x) on the reals or on the circle T (continuous and 2π periodic) we say that f(x) belongs to the generalized Lipschitz class, denoted by f ∈ Lip* α, if

where and Δhf(x) = f(x + ½h)−f(x−½h). For a convolution approximation process given by

where

we shall investigate equivalence relations between the asymptotic behaviour of (d/dx)rAn(f, x) and f ∈ Lip* α.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 1 , July 1981 , pp. 51 - 61
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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