Approximation properties and error estimation of q-Bernstein shifted operators

被引：35

作者：

Mursaleen, Mohammad ^{[1
]}

Ansari, Khursheed J. ^{[2
]}

Khan, Asif ^{[1
]}

机构：

[1] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

[2] King Khalid Univ, Dept Math, Coll Sci, Abha 61413, Saudi Arabia

来源：

NUMERICAL ALGORITHMS | 2020年 / 84卷 / 01期

关键词：

Lupas q-Bernstein shifted operators; Rate of convergence; Modulus of continuity; Voronovskaja type theorem; K-functional; Local approximation; STATISTICAL APPROXIMATION; (P; Q)-ANALOG; THEOREMS;

D O I：

10.1007/s11075-019-00752-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, q-analogue of Lupas Bernstein operators with shifted knots are introduced. First, some basic results for convergence of the introduced operators are established and then the rate of convergence by these operators in terms of the modulus of continuity are obtained. Further, a Voronovskaja type theorem and local approximation results for the said operators are studied. Error estimation tables are presented with respect to different parameters. We also show comparisons by some illustrative graphics for the convergence of operators to a function with the help of MATLAB R2018a.

引用

页码：207 / 227

页数：21

共 29 条

[1] Approximation by Bivariate (p, q)-Bernstein-Kantorovich Operators [J].

Acar, Tuncer ;

Aral, Ali ;

Mohiuddine, S. A. .

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2018, 42 (A2) :655-662

[2] (p,q)-Generalization of Szasz-Mirakyan operators [J].

Acar, Tuncer .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (10) :2685-2695

[3]

Acar T, 2016, J INEQUAL APPL, DOI 10.1186/s13660-016-1045-9

[4]

Altomare F., 1994, APPENDIX MICHAEL PAN, VVolume 17

[5]

Aral A., 2013, Applications of Q-Calculus in Operator Theory

[6]

Bernstein S., 1912, Commun. Soc. Math. Charkow Ser., V13, P1

[7] On (p, q)-analogue of Kantorovich type Bernstein-Stancu-Schurer operators [J].

Cai, Qing-Bo ;

Zhou, Guorong .

APPLIED MATHEMATICS AND COMPUTATION, 2016, 276 :12-20

[8]

Derriennic MM., 2005, Rend. Circ. Mat. Palermo, VII, P269

[9]

Devore R. A., 1993, Constructive Approximation

[10] On statistical approximation properties of the Kantorovich type Lupas operators [J].

Dogru, Ogun ;

Kanat, Kadir .

MATHEMATICAL AND COMPUTER MODELLING, 2012, 55 (3-4) :1610-1621

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