Approximation by complex Favard-Szász-Mirakjan-Stancu operators in compact disks

被引：12

作者：

Gupta V. ^{[1
]}

K Verma D. ^{[2
]}

机构：

[1] School of Applied Sciences, Netaji Subhas Institute of Technology, Sector 3 Dwarka, New Delhi

[2] Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee

来源：

Mathematical Sciences | 2012年 / 6卷 / 1期

关键词：

30E10; 41A25; 41A28; Complex Favard-Szász-Mirakjan-Stancu operators; Exact order of approximation in compact disks; Simultaneous approximation; Voronovkaja-type result;

D O I：

10.1186/2251-7456-6-25

中图分类号：

学科分类号：

摘要：

Purpose: The purpose of the present paper is to study the Stancu-type generalization of complex Favard-Szász-Mirakjan operators and establish some approximation results in complex domain. Methods: It is observed that the complex Favard-Szász-Mirakjan-Stancu operators can be written in the form of divided differences. Thus, it is possible to study such operators in complex domain. We use analytical method to obtain our results. Results: We have estimated the order of simultaneous approximation, Voronovskaja-type results with quantitative estimates for the complex Favard-Szász-Mirakjan-Stancu operators attached to analytic functions on compact disks. Also, some estimates on the rate of convergence are given. Conclusions: The results proposed here are new and have better rate of convergence. © 2012, Gupta and Verma; licensee Springer.

引用

共 17 条

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