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

共 50 条

[1] Convergence of λ-Bernstein operators based on (p, q)-integers
Cai, Qing-Bo
Cheng, Wen-Tao
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2020, 2020 (01)
[2] Convergence of λ-Bernstein operators based on (p, q)-integers
Qing-Bo Cai
Wen-Tao Cheng
Journal of Inequalities and Applications, 2020
[3] ON THE CONVERGENCE OF (p, q)-BERNSTEIN OPERATORS OF THE RATIONAL FUNCTIONS WITH POLES IN [0,1]
Khan, Faisal
Saif, Mohd
Mursaleen, M.
Khan, Abdul Hakim
TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2020, 10 : 15 - 27
[4] On the convergence of Lupa (p,q)-Bernstein operators via contraction principle
Bin Jebreen, Haifa
Mursaleen, Mohammad
Ahasan, Mohd
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2019,
[5] Convergence of Iterates of q-Bernstein and (p,q)-Bernstein Operators and the Kelisky-Rivlin Type Theorem
Rahman, Shagufta
Mursaleen, M.
Alkhaldi, Ali H.
FILOMAT, 2018, 32 (12) : 4351 - 4364
[6] On (p, q)-analogue of Bernstein operators
Mursaleen, M.
Ansari, Khursheed J.
Khan, Asif
APPLIED MATHEMATICS AND COMPUTATION, 2015, 266 : 874 - 882
[7] Uniform and pointwise convergence of Bernstein-Durrmeyer operators with respect to monotone and submodular set functions
Gal, Sorin G.
Opris, Bogdan D.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 424 (02) : 1374 - 1379
[8] UNIFORM APPROXIMATION BY GENERALIZED Q-BERNSTEIN OPERATORS
Finta, Z.
MISKOLC MATHEMATICAL NOTES, 2017, 17 (02) : 877 - 891
[9] ON CONVERGENCE OF BERNSTEIN POLYNOMIALS FOR SOME UNBOUNDED ANALYTIC FUNCTIONS
TONNE, PC
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 22 (01) : 1 - &
[10] APPROXIMATION OF ANALYTIC FUNCTIONS BY BERNSTEIN-TYPE OPERATORS
EISENBER.SM
WOOD, B
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 17 (01): : 94 - &

← 1 2 3 4 5 →