On the best approximation of vector valued functions by polynomials with coefficients in vector spaces |
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Authors: | George A. Anastassiou Sorin G. Gal |
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Affiliation: | (1) Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, USA;(2) Department of Mathematics, University of Oradea, Str. Armatei Romane 5, 410087 Oradea, Romania |
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Abstract: | In this paper, we prove some basic results concerning the best approximation of vector-valued functions by algebraic and trigonometric polynomials with coefficients in normed spaces, called generalized polynomials. Thus we obtain direct and inverse theorems for the best approximation by generalized polynomials and results concerning the existence (and uniqueness) of best approximation generalized polynomials. This paper was written during the 2005 Spring Semester when the second author (S.G. Gal) was a Visiting Professor at the Department of Mathematical Sciences, The University of Memphis, TN, USA. Mathematics Subject Classification (2000) 41A65, 41A17, 41A27 |
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Keywords: | Vector-valued functions Generalized polynomials Best approximation Direct and inverse theorems |
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