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Approximation of vector-valued functions by polynomials with coefficients in normed spaces applications

Anastassiou G., Gal S.

Demonstratio Mathematica

2006

Vol. 39, nr 3

539-552

In this paper we prove basic results in the approximation of vector-valued functions by polynomials with coefficients in normed spaces, called generalized polynomials. Thus we obtain : estimates in terms of Ditzian-Totik Lp-moduli of smoothness for approximation by Bernstein-Kantorovich generalized polynomials and by other kinds of operators like the Szasz-Mirakian operators, Baskakov operators, Post-Widder operators and their Kantorovich analogues and inverse theorems for these operators. Applications to approximation of random functions and of fuzzy-number-valued functions are given.