International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1978 / Article

Open Access

Volume 1 |Article ID 401670 | 14 pages | https://doi.org/10.1155/S0161171278000411

Uniform approximation by incomplete polynomials

Received05 Jun 1978

Abstract

For any θ with 0<θ<1, it is known that, for the set of all incomplete polynomials of type θ, i.e, {p(x)=k=snakxk:sθn}, to have the Weierstrass property on [aθ,1], it is necessary that θ2aθ1. In this paper, we show that the above inequalities are essentially sufficient as well.

Copyright © 1978 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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