Some approximation results involving the q-Szasz-Mirakjan-Kantorovich type operators via Dunkl's generalization

被引：53

作者：

Srivastava, H. M. ^{[1
,2
]}

Mursaleen, M. ^{[3
,5
]}

Alotaibi, Abdullah M. ^{[4
,5
]}

Nasiruzzaman, Md. ^{[3
]}

Al-Abied, A. A. H. ^{[3
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[3] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

[4] King Abdulaziz Univ, Dept Math, Fac Sci, POB 80203, Jeddah 21589, Saudi Arabia

[5] King Abdulaziz Univ, Dept Math, Operator Theory & Applicat Res Grp, Fac Sci, POB 80203, Jeddah 21589, Saudi Arabia

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 15期

关键词：

basic (or q-) integers; basic (or q-) hypergeometric functions; basic (or q-) exponential functions; q-Dunkl's analogue; Szasz operator; q-Szasz-Mirakjan-Kantorovich operator; rate of convergence; modulus of continuity; Peetre's K-functional; STATISTICAL APPROXIMATION; POLYNOMIALS;

D O I：

10.1002/mma.4397

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to introduce a family of q-Szasz-Mirakjan-Kantorovich type positive linear operators that are generated by Dunkl's generalization of the exponential function. We present approximation properties with the help of well-known Korovkin's theorem and determine the rate of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K-functional, and the second-order modulus of continuity. Furthermore, we obtain the approximation results for bivariate q-Szasz-Mirakjan-Kantorovich type operators that are also generated by the aforementioned Dunkl generalization of the exponential function. Copyright (c) 2017 John Wiley & Sons, Ltd.

引用

页码：5437 / 5452

页数：16

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