Statistical approximation properties of q-Bleimann, Butzer and Hahn operators

被引：31

作者：

Ersan, Sibel ^{[2
]}

Dogru, Ogun ^{[1
]}

机构：

[1] Gazi Univ, Fac Sci & Arts, Dept Math, TR-06500 Ankara, Turkey

[2] Cankaya Univ, Fac Sci & Arts, Dept Math & Comp Sci, TR-06530 Ankara, Turkey

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2009年 / 49卷 / 7-8期

关键词：

Linear positive operators; Statistical convergence; q-Bleimann; Butzer and Hahn operators; Rate of statistical convergence; Modulus of continuity; Lipschitz type maximal functions;

D O I：

10.1016/j.mcm.2008.10.008

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The main aim of this study is to introduce a new generalization of q-Bleimann, Butzer and Hahn operators and obtain statistical approximation properties of these operators with the help of the Korovkin type statistical approximation theorem. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function are also established. Our results show that rates of convergence of our operators are at least as fast as classical BBH operators. The second aim of this study is to construct a bivariate generalization of the operator and also obtain the statistical approximation properties. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：1595 / 1606

页数：12

共 17 条

[1] Altomare F., 2011, Korovkin-Type Approximation Theory and its Applications
[2] Anastassiou G.A., 2000, Approximation Theory
[3] Andrews G.E., 1999, SPECIAL FUNCTIONS
[4] [Anonymous], INDAG MATH
[5] [Anonymous], 2006, P INT C NUMERICAL AN
[6] [Anonymous], 1990, Approximation Theory
[7] Bleimann, Butzer, and Hahn operators based on the q-integers
Aral, Ali
Dogru, Oguen
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2007, 2007 (1)
[8] Dogru O., 2005, Georgian Mathematical J., V12, P415
[9] A-statistical extension of the Korovkin type approximation theorem
Erkus, E
Duman, O
[J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2005, 115 (04): : 499 - 508
[10] Ersan S, 2007, APPLIED MATHEMATICS FOR SCIENCE AND ENGINEERING, P122

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