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Scientific paper ID 1217 : 2015/3
WEIGHTED APPROXIMATION OF FUNCTIONS BY MEYER - KONIG AND ZELLER OPERATORS
Ivan Gadjev In this article we characterize the weighted error of approximation of functions by Meyer-Kӧnig and Zeller operators with weight w=(1-x)(-1). Using the closed connection between the operators of Meyer-Kӧnig and Zeller and the operator of Baskakov, we prove that the weighted error of approximation by Meyer-Kӧnig and Zeller operators with weight w=〖(1-x)〗^(-1), is equivalent to the weighted K-functional, consequently, to the appropriate modulus of smoothness of Ditzian and Totik.
Майер-Кьониг и Целер Баскаков К-функционал. Анотация: В статията се характеризира грешката на приближение на функции с оператора на Майер-Кьониг и Целер при тегло w=〖(1-x)〗Meyer-Kӧnig and Zeller Baskakov K-functional.Ivan Gadjev BIBLIOGRAPHY [1] Baskakov V. A. An instance of a sequence of the linear positive operators in the space of continuous functions. Docl. Akad. Nauk SSSR, 113:249_251. [2] W. Meyer-K_onig and K. Zeller. Bernsteinsche Potenzreihen. Studia Math., 19:89_94. [3] I. Gadjev. Strong converse result for Baskakov operator. Serdica Math. Journal, 40:273_318. [4] V. Totik. Uniform aproximation by Baskakov and Meyer-K_onig and Zeller-type operators. Period. Math. Hungar, 14(3-4):209_ 228, 1983. [5] K. G. Ivanov and P. E. Parvanov. Weighted approximation by Meyer-K_onig and Zeller-Type operators. Proceedings Volume of CTF-2010, Sozopol, Bulgaria ( dedicated to the memory of Borislav Bojanov)., pages 150_160, 2011 [6] Z. Ditzian and V. Totik. Moduli of Smoothness. Springer, Berlin, New York, 1987. |
