Lipschitz classes and convolution approximation processes
Published online by Cambridge University Press: 24 October 2008
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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