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

• Autorzy: Anastassiou G. , Gal S.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

vector valued functions; generalized polynomials; inverse theorems; random approximation; fuzzy approximation

PL

funkcje wektorowe; wielomiany współrzędne; teoria odwrotna; aproksymacja losowa; aproksymacja rozmyta

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 3
• Strony: 539--552
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Anastassiou G.

autor

Gal S.

• The University of Memphis, Department of Mathematical Sciences, Memphis, TN, 38152, USA,

Bibliografia

• [1] G. A. Anastassiou and S. G. Gal, Shape preserving approximation in vector ordered spaces, Appl. Math. Lett. 18 (2005), 1408-1411.
• [2] G. A. Anastassiou and S. G. Gal, On the best approximation of vector valued functions by polynomials with coefficients in vector spaces, Ann. Mat. Pura ed Appl., accepted for publication.
• [3] G. A. Anastassiou and S. G. Gal, Geometric and approximation properties of complex generalized singular integrals in the unit disk, J. Korean Math. Soc., accepted for publication.
• [4] Z. Ditzian and V. Totik, Moduli of Smoothness, Springer-Verlag, Berlin, New York, 1987.
• [5] D. Dubois, H. Prade, Fuzzy numbers: An overview, Analysis of fuzzy information, vol. 1: Math. Logic, CRC Press, Boca Raton, 3-39, 1987.
• [6] S. G. Gal, Remarks on the approximation of normed spaces valued functions by some linear operators, Proceeding of the 6th Romanian-German Research Seminar, RoGer 2004 (H.H. Gonska et al Edt.), Mathematical Analysis and Approximation Theory, Mediamira Science Publisher, Cluj, 2005, pp. 99-109.
• [7] S. G. Gal, Global Smoothness and Shape Preserving Interpolation by Classical Operators, Birkhauser, Boston, Basel, Berlin, 2005.
• [8] S. G. Gal, Approximation Theory in Random Setting, Chapter 12 in : Handbook of Analytic-Computational Methods in Applied Mathematics (G.A. Anastassiou ed.), Chapman and Hall/CRC, Boca Raton, London, New York, Washington D.C., 2000, 571-616.
• [9] S. G. Gal, Approximation Theory in Fuzzy Setting, Chapter 13 in : Handbook of Analytical-Computational Methods in Applied Mathematics (G.A. Anastassiou ed.), Chapman and Hall/CRC, Boca Raton, London, New York, Washington D.C., 2000.
• [10] Wu Congxin and Gong Zengtai, On Henstock integral of fuzzy-number-valued functions, I, Fuzzy Sets and Systems, 115(2000), no. 3 , 377-391.
• [11] L.A. Zadeh, Fuzzy Sets, Inform. and Control 8 (1965), 338-353.