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Universality of methods approximating the derivative
Published online by Cambridge University Press: 17 April 2009
Extract
We prove the existence of universal functions for mappings Tn: C([0,1]) → Lp([0,1]), 0 < p < 1, with Tn(f) → f′ (n → ∞) on certain subsets of C1([0,1]). As an application we conclude that there are continuous functions f ∈ C([0,1]), such that the derivatives of the Bernstein polynomials form a dense subset of Lp([0,1]) for each 0 < p < 1.
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- Research Article
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- Copyright © Australian Mathematical Society 2006