Approximation of vector-valued functions by polynomials with coefficients in normed spaces and Applications
Abstract
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 Szász-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.
Publication Title
Demonstratio Mathematica
Recommended Citation
Anastassiou, G., & Gal, S. (2006). Approximation of vector-valued functions by polynomials with coefficients in normed spaces and Applications. Demonstratio Mathematica, 39 (3), 539-552. https://doi.org/10.1515/dema-2006-0309
