Statistical approximation of certain positive linear operators constructed by means of the Chan-Chyan-Srivastava polynomials

被引：77

作者：

Erkus, Esra

Duman, Oktay

Srivastava, H. M. ^{[1
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada

[2] Ankara Univ, Fac Sci, Dept Math, TR-06100 Ankara, Turkey

[3] Canakkale Onsekiz Mart Univ, Fac Sci & Arts, Dept Math, TR-17020 Terzioglu Kampusu, Canakkale, Turkey

[4] TOBB Univ Econ & Technol, Fac Arts & Sci, Dept Math, TR-06530 Ankara, Turkey

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2006年 / 182卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Chan-Chyan-Srivastava multivariable polynomials; Lagrange polynomials; A-statistical convergence; positive linear operators; Korovkin approximation theorem; Fourier series; Gibbs phenomenon; modulus of continuity; lipschitz class;

D O I：

10.1016/j.amc.2006.01.090

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this study, by obtaining some Korovkin type approximation results in statistical sense for certain positive linear operators constructed by means of the Chan-Chyan-Srivastava multivariable polynomials [W.-C.C. Chan, C.-J. Chyan, H.M. Srivastava, The Lagrange polynomials in several variables, Integral Transform. Spec. Funct. 12 (2001) 139-148], we show that our approximation method is stronger than the corresponding classical aspects in the approximation theory settings. Furthermore, we investigate their statistical rates by means of the modulus of continuity and the elements of the Lipschitz class. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：213 / 222

页数：10

共 13 条

[1]

BOJANIC R., 1992, J NAT SCI MATH, V32, P5

[2]

Boos J., 2000, CLASSICAL MODERN MET

[3] The Lagrange polynomials in several variables [J].

Chan, WCC ;

Chyan, CJ ;

Srivastava, HM .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2001, 12 (02) :139-148

[4]

Duman O, 2003, MATH INEQUAL APPL, V6, P689

[5]

Erdelyi A, 1955, HIGHER TRANSCENDENTA, V3

[6]

ERKUS E, 2006, IN PRESS STUD SCI MA, V43

[7]

Fast H., 1951, Colloq. Math, V2, P241, DOI [10.4064/cm-2-3-4-241-244, DOI 10.4064/CM-2-3-4-241-244]

[8] DENSITIES AND SUMMABILITY [J].

FREEDMAN, AR ;

SEMBER, JJ .

PACIFIC JOURNAL OF MATHEMATICS, 1981, 95 (02) :293-305

[9]

Fridy JA., 1985, Analysis, V5, P301, DOI DOI 10.1524/ANLY.1985.5.4.301

[10] Some approximation theorems via statistical convergence [J].

Gadjiev, AD ;

Orhan, C .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2002, 32 (01) :129-138

← 1 2 →