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
收藏
页码：505 / 514
页数：10
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