On Some Statistical Approximation by (p, q)-Bleimann, Butzer and Hahn Operators

被引:14
作者
Ansari, Khursheed J. [1 ]
Ahmad, Ishfaq [1 ,2 ]
Mursaleen, M. [3 ]
Hussain, Iqtadar [4 ]
机构
[1] King Khalid Univ, Dept Math, Coll Sci, Abha 61413, Saudi Arabia
[2] Int Islamic Univ, Dept Math & Stat, Islamabad 44000, Pakistan
[3] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India
[4] Qatar Univ, Dept Math Stat & Phys, Doha 2713, Qatar
来源
SYMMETRY-BASEL | 2018年 / 10卷 / 12期
关键词
q-Bleimann-Butzer-Hahn operators; (p; q)-integers; q)-Bernstein operators; q)-Bleimann-Butzer-Hahn operators; modulus of continuity; rate of approximation; K-functional; Q)-ANALOG;
D O I
10.3390/sym10120731
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this article, we propose a different generalization of (p,q)-BBH operators and carry statistical approximation properties of the introduced operators towards a function which has to be approximated where (p,q)-integers contains symmetric property. We establish a Korovkin approximation theorem in the statistical sense and obtain the statistical rates of convergence. Furthermore, we also introduce a bivariate extension of proposed operators and carry many statistical approximation results. The extra parameter p plays an important role to symmetrize the q-BBH operators.
引用
收藏
页数:15
相关论文
共 28 条
[1]   (p,q)-Generalization of Szasz-Mirakyan operators [J].
Acar, Tuncer .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (10) :2685-2695
[2]  
Anastassiou G.A., 2000, Approximation Theory
[3]  
[Anonymous], 1990, Approximation Theory
[4]  
Ansari K.J., 2015, THESIS
[5]  
Ansari KJ, 2017, INT J NONLINEAR ANAL, V8, P181, DOI 10.22075/ijnaa.2017.1827.1479
[6]   Bleimann, Butzer, and Hahn operators based on the q-integers [J].
Aral, Ali ;
Dogru, Oguen .
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2007, 2007 (1)
[7]  
BLEIMANN G, 1980, P K NED AKAD A MATH, V83, P255
[8]  
Dattoli G., 2016, J COMPUT ANAL APPL, V8, P369
[9]  
Ersan S, 2007, APPLIED MATHEMATICS FOR SCIENCE AND ENGINEERING, P122
[10]  
Fast H, 1951, Colloquium Mathematicae, V2, P241