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

[11] Korovkin type approximation theorems obtained through generalized statistical convergence [J].

Edely, Osama H. H. ;

Mohiuddine, S. A. ;

Noman, Abdullah K. .

APPLIED MATHEMATICS LETTERS, 2010, 23 (11) :1382-1387

[12] Approximation properties of a new type Bernstein-Stancu polynomials of one and two variables [J].

Gadjiev, A. D. ;

Ghorbanalizadeh, A. M. .

APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (03) :890-901

[13]

Gairola AR, 2016, P NATL A SCI INDIA A, V86, P229, DOI 10.1007/s40010-016-0267-z

[14]

Kac VG., 2002, QUANTUM CALCULUS UNI

[15] Chlodowsky type generalization of (p,q)-Szasz operators involving Brenke type polynomials [J].

Kadak, Ugur ;

Mishra, Vishnu Narayan ;

Pandey, Shikha .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2018, 112 (04) :1443-1462

[16] Weighted statistical convergence based on generalized difference operator involving (p, q)-gamma function and its applications to approximation theorems [J].

Kadak, Ugur .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 448 (02) :1633-1650

[17] On weighted statistical convergence based on (p, q)-integers and related approximation theorems for functions of two variables [J].

Kadak, Ugur .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 443 (02) :752-764

[18] Bezier curves based on Lupas (p, q)-analogue of Bernstein functions in CAGD [J].

Khan, Khalid ;

Lobiyal, D. K. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 317 :458-477

[19]

Korovkin PP, 1953, DOKL AKAD NAUK SSSR, V90, P961

[20]

Lorentz G. G., 1953, American Mathematical Soc., V8

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