A complete extension of the Bernstein–Weierstrass Theorem to the infinite interval (-∞,+∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {(-\infty ,+\infty )}$$\end{document} via Chlodovsky polynomials

被引：0
作者：
Harun Karsli
机构：
[1] Bolu Abant Izzet Baysal University,Faculty of Science and Arts, Department of Mathematics
来源：
Advances in Operator Theory | 2022年 / 7卷 / 2期
关键词：
Chlodovsky polynomials; Rate of convergence; Modulus of continuity; Peetre K-functional; Lipschitz space; Voronovskaya type theorem; 41A10; 41A25; 41A36;
D O I：
10.1007/s43036-021-00178-7
中图分类号：
学科分类号：
摘要：
In the present paper, we consider the very recently introduced Chlodovsky operators on the real line by Abel and Karsli (Mediterr J Math 17:201, 2020). We study some approximation properties of these new operators, which include the rate of convergence and a Voronovskaya type theorem.
引用
收藏
相关论文
共 25 条
  • [1] Abel U(2018)Asymptotic expansions for Bernstein–Durrmeyer–Chlodovsky polynomials Results Math. 73 104-7
  • [2] Karsli H(2020)A complete asymptotic expansion for Bernstein–Chlodovsky polynomials for functions on Mediterr. J. Math. 17 201-164
  • [3] Abel U(1960)On a generalization of the theorem of Voronovskaya Zeszyty Naukowe UAM Poznan. 2 1-346
  • [4] Karsli H(2010)Korovkin-type theorems and approximation by positive linear operators Surv. Approx. Theory 5 92-553
  • [5] Albrycht J(2003)Convergence in variation and rates of approximation for Bernstein-type polynomials and singular convolution integrals Analysis (Munich) 23 299-58
  • [6] Radecki J(1954)On the extension of Bernstein polynomials to the infinite interval Proc. Am. Math. Soc. 5 547-393
  • [7] Altomare F(2009)Voronovskaya-type theorems for derivatives of the Bernstein–Chlodovsky polynomials and the Szasz–Mirakyan operator Comment. Math. 49 33-786
  • [8] Bardaro C(1937)Sur le développement des fonctions dé finies dans un intervalle infini en séries de polynomes de M. S. Bernstein Compos. Math. 4 380-127
  • [9] Butzer PL(1976)Theorems of the type of P. P. Korovkin’s theorems Mat. Zametki. 20 781-142
  • [10] Stens RL(1989)Direct and converse results for operators of Baskakov–Durrmeyer type Approx. Theory Appl. 5 105-436
123