ON APPROXIMATION BY FELLER OPERATORS FOR FUNCTIONS HAVING DISCONTINUITY POINTS OF THE FIRST KIND

Guo Shun-sheng

Acta Mathematicae Applicatae Sinica ›› 1991, Vol. 14 ›› Issue (1) : 57-65.

PDF(480 KB)
中国科学院数学与系统科学研究院期刊网
PDF(480 KB)
Acta Mathematicae Applicatae Sinica ›› 1991, Vol. 14 ›› Issue (1) : 57-65. DOI: 10.12387/C1991008

ON APPROXIMATION BY FELLER OPERATORS FOR FUNCTIONS HAVING DISCONTINUITY POINTS OF THE FIRST KIND

  • Guo Shun-sheng
Author information +
History +

Abstract

In this paper, we investigate the degree of approximation by Feller operators for functions which have only discontinuity points of the first kind on [0, ∞) with exponential growth. Our estimates are essentially the best possible. The results here include the results or partial results of the references [2, 3, 6, 7, 9].

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations
Guo Shun-sheng. ON APPROXIMATION BY FELLER OPERATORS FOR FUNCTIONS HAVING DISCONTINUITY POINTS OF THE FIRST KIND. Acta Mathematicae Applicatae Sinica, 1991, 14(1): 57-65 https://doi.org/10.12387/C1991008

References

[1] F. Herzog and J. D. Hill, The Bernstein Polynomials for Discontinuous Functions, Atner. J.Math., 6B (1946), 109-124.
[2] F. Cheng, On the Rate of Convergence of Bernstein Polyno mials of Functions of Bounded Variation.J. Approx. Th., 39(1983), 259-274.
[3] 陈文忠, 郭顺生, 某些正线性算子对有界变差函数的点态逼近度, 高等学校计算数学学报, 9:3(1987), 243-250.
[4] 郭顺生, 关于SBK算子对有界变差函数的点态逼近度, 科学通报, 20(1986), 1521-1526(中文版);32(1987), 1297-1303(外文版).
[5] R. Bojanic, and M. Vuilleumier. On the Rate of Convergence of Fourier-Legendre Series of Functions of Bounded Variation, J. Appror. Th., 31 (1981), 67-79.
[6] F. Cheng, On the Rate of Convergence of the Szasz-Mirakyan Operator for Functions of Bounded Variation, J. Approx. Th., 40(1984), 226-241.
[7] 陈文忠, 郭顺生, On the rate of the Gamma operator for functions of bounded variation, Approx.Th.& its Appl. 1:5 (1985), 85-96.
[8] 郭顺生, On the Rate of Convergence of the Durrmeyer Operator for Functions of Bounded Variation, J. Approx. Th., 51 (1987), 183-192.
[9] 王美琴, 周信龙, 李武, Bernstein算子逼近第一类间断点的函数, 杭州大学学报(自然版)14:3(1987), 265-271.
[10] W. Feller, An Introduction to Probability Theory and Its Applications. John Willey, 1966.
[11] R.A.Khan. On the Lp Norm for Some Approximation Operators, J. Approx. Th., 45 (1985), 339-345.
[12] R. A. Khan. Some Probabilistic Methods in the Theory of Approximation Operators:Acro Math. Aead. Scien. Hung., 35(1980), 193-203.
[13] 王梓坤, 概率论基础及其应用, 科学出版社, 北京, 1979.
PDF(480 KB)

274

Accesses

0

Citation

Detail
Sections
Recommended

/

〈 〉