APPROXIMATION OF CONTINUOUS FUNCTIONS BY MONOTONE SEQUENCES OF POLYNOMIALS WITH RESTRICTED COEFFICIENTS

S.G. Gal

Abstract: The problem of approximation by polynomials with restricted coefficients, is considered in several papers (e.g. [7--9]). In [1--6], I have proved among other things, that every $f\i C_{[0,1]}$ can be approximated uniformly by a polynomial sequence $(P_n)_n$ such that $(P_n)_n$ is monotonically decreasing on $[0,1]$. The aim of this paper is to extend the ideas of [1--6] to the case of approximation by polynomials with restricted coeficients.

Classification (MSC2000): 41A10; 41A29

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