Title

Existence of Best n-Convex Approximations in L1

Document Type

Article

Publication Date

1989

Publication Source

Journal of Approximation Theory and Applications

Volume

5

Issue

2

Inclusive pages

51-57

Abstract

We consider here best approximation by n-convex functions. We first show that if f∈L1[0,1], then there is, a best L1-approximant to f by functions which are n-convex on (0,1). We then show that if f∈L∞[0,1], then any best Lp-approximant, fp, to f by n-convex, functions is bounded and hence, f has the Pólya-one property, i.e., fp converges a.e. as p decreases to one.

Disciplines

Mathematics

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