ON ESTIMATION OF UNIFORM CONVERGENCE OF ANALYTIC FUNCTIONS BY (p, q)-BERNSTEIN OPERATORS

被引：2

作者：

Mursaleen, M. ^{[1
]}

Khan, Faisal ^{[1
]}

Saif, Mohd ^{[2
]}

Khan, Abdul Hakim ^{[2
]}

机构：

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

[2] Aligarh Muslim Univ, Dept Appl Math, Aligarh, Uttar Pradesh, India

来源：

KOREAN JOURNAL OF MATHEMATICS | 2019年 / 27卷 / 02期

关键词：

(p; q)-integers; q)-Bernstein operators; divided difference; analytic function; uniform convergence; Q-BERNSTEIN POLYNOMIALS; APPROXIMATION; Q)-ANALOG;

D O I：

10.11568/kjm.2019.27.2.505

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the approximation properties of a continuous function by the sequence of (p, q)-Bernstein operators for q > p > 1. We obtain bounds of (p, q)-Bernstein operators. Further we prove that if a continuous function admits an analytic continuation into the disk {z : vertical bar z vertical bar <= rho, then B-p,q(n)(g; z) -> g(z) (n -> infinity) uniformly on any compact set in the given disk {z : vertical bar z vertical bar <= rho}, rho > 0.

引用

页码：505 / 514

页数：10

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