Approximation of bounded continuous functions by linear combinations of Phillips operators

• Autorzy: Tachev G.
• Języki publikacji: EN

Abstrakty

EN

We study the approximation properties of linear combinations of the so-called Phillips operators, which can be considered as genuine Szász–Mirakjan–Durrmeyer operators. As main result, we prove a direct estimate for the rate of approximation of bounded continuous functions (…), measured in (…)-norm and thus generalizing the results, proved earlier by Gupta, Agrawal, and Gairola in [3]. Our estimates rely on the recent results, obtained in the joint works of M. Heilmann and the author [10, 11].

Słowa kluczowe

EN

linear combinations; Phillips operators; simultaneous approximation; Ditzian–Totik moduli of smoothness

PL

kombinacje liniowe; operatory Philipsa; aproksymacja jednoczesna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 3
• Strony: 662--671
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Tachev G.

• University of Architecture,s Dept. of Mathematics, 1 Hristo Smirnenski, Blvd., 1046-Sofia, Bulgaria

Bibliografia

• [1] P. N. Agrawal, V. Gupta, On the iterative combinations of Phillips operators, Bull. Inst. Math. Acad. Sinica 18(4) (1990), 361–368.
• [2] P. N. Agrawal, V. Gupta, On convergence of derivatives of Phillips operators, Demonstratio Math. 27 (1994), 501–510.
• [3] P. N. Agrawal, V. Gupta, A. R. Gairola, On derivatives of an iterative combinations of Phillips operators, Nonlinear Funct. Anal. Appl. 12(2) (2007), 195–203.
• [4] Z. Ditzian, V. Totik, Moduli of Smoothness, Spriner Verlag, New York, 1987.
• [5] N. K. Govil, V. Gupta, M. A. Noor, Simultaneous approximation for the Phillips operators, Int. J. Math. Math. Sci., Article ID 49094, Pages 19, (2006).
• [6] V. Gupta, P. N. Agrawal, Linear combinations of Phillips operators, Indian Acad. Math. 11(2) (1989), 106–114.
• [7] V. Gupta P. N. Agrawal, Lp-approximation by iterative combination of Phillips operators, Publ. Inst. Math. 52(66) (1992), 67–76.
• [8] V. Gupta, A. Sahai, On the linear combinations of Phillips operators, Soochow J. Math. 19(3) (1993), 313–323.
• [9] M. Heilmann, Erhöhung der Konvergenzgeschwindigkeit bei der Approximation von Funktionen mit Hilfe von Linearkombinationen spezieller positiver linear Operatoren, Habilitationsschrift, Universität Dortmund, (1991).
• [10] M. Heilmann, G. Tachev, Commutativity, direct and strong converse results for Phillips operators, East J. Approx. 17(3) (2011), 299–317.
• [11] M. Heilmann, G. Tachev, Linear combinations of genuine Szasz-Mirakjan-Durrmeyer operators, Springer Proceedings in Mathematics and Statistics with Volume title Advances in Applied Mathematics and Approximation Theory-Contributions from AMAT 2012 Conference, Turkey, ed. by G. Anastassiou and O. Duman, (2012), 5-th Chapter, 85–106.
• [12] C. P. May, On Phillips operator, J. Approx. Theory 20 (1997), 315–332.
• [13] A. F. Timan, Theory of Approximation of Functions of a Real Variable, English translation 1963, Pergamon Press, The MacMillian co.