Approximation by a kind of complex modified q-Durrmeyer type operators in compact disks

被引：7

作者：

Ren, Mei-Ying ^{[1
]}

Zeng, Xiao-Ming ^{[2
]}

机构：

[1] Wuyi Univ, Dept Math & Comp Sci, Wuyishan 354300, Peoples R China

[2] Xiamen Univ, Dept Math, Xiamen 361005, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2012年

基金：

中国国家自然科学基金;

关键词：

complex modified q-Durrmeyer type operators; simultaneous approximation; Voronovskaja-type result; overconvergence; q-calculus; SZASZ-MIRAKJAN OPERATORS; Q-INTEGERS; STATISTICAL APPROXIMATION; ZELLER OPERATORS; PRESERVE X(2); MEYER-KONIG; POLYNOMIALS;

D O I：

10.1186/1029-242X-2012-212

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, in order to make the convergence faster to a function being approximated, we introduce a kind of complex modified q-Durrmeyer type operators which can reproduce constant and linear functions. We study the approximation properties of these operators. We obtain the order of simultaneous approximation and a Voronovskaja-type result with a quantitative estimate for these complex modified q-Durrmeyer type operators attached to analytic functions on compact disks. More important, our results show the overconvergence phenomenon for these complex operators.

引用

页数：14

共 17 条

[1] On q-analogue of a complex summation-integral type operators in compact disks [J].

Agarwal, Ravi P. ;

Gupta, Vijay .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012, :1-13

[2] On a generalization of Bleimann, Butzer and Hahn operators based on q-integers [J].

Agratini, Octavian ;

Nowak, Grzegorz .

MATHEMATICAL AND COMPUTER MODELLING, 2011, 53 (5-6) :699-706

[3] A generalization of Szasz-Mirakyan operators based on q-integers [J].

Aral, Ali .

MATHEMATICAL AND COMPUTER MODELLING, 2008, 47 (9-10) :1052-1062

[4] Statistical approximation by a modification of q-Meyer-Konig and Zeller operators [J].

Dogru, Oguen ;

Orkcu, Mediha .

APPLIED MATHEMATICS LETTERS, 2010, 23 (03) :261-266

[5] King type modification of Meyer-Konig and Zeller operators based on the q-integers [J].

Dogru, Oguen ;

Orkcu, Mediha .

MATHEMATICAL AND COMPUTER MODELLING, 2009, 50 (7-8) :1245-1251

[6] VORONOVSKAJA'S THEOREM, SHAPE PRESERVING PROPERTIES AND ITERATIONS FOR COMPLEX q-BERNSTEIN POLYNOMIALS [J].

Gal, Sorin G. .

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2011, 48 (01) :23-43

[7]

Gasper G, 1990, BASCI HYPERGEOMETRIC, V35

[8] The rate of convergence of q-Durrmeyer operators for 0<q<1 [J].

Gupta, Vijay ;

Heping, Wang .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2008, 31 (16) :1946-1955

[9] Statistical approximation properties of q-Baskakov-Kantorovich operators [J].

Gupta, Vijay ;

Radu, Cristina .

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2009, 7 (04) :809-818

[10]

Kac V. G., 2002, Quantum Calculus, V113

← 1 2 →