Bernstein-Schurer-Durrmeyer type operators for functions of one and two variables

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• 作者：Arun Kajla^a ; ^{rachitkajla47@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Nurhayat Ispir^b ; ^{nispir@gazi.edu.tr" class="auth_mail" title="E-mail the corresponding author} ; P.N. Agrawal^a ; ^{pna_iitr@yahoo.co.in" class="auth_mail" title="E-mail the corresponding author} ; Meenu Goyal ; ^a ; ^{meenu.goyal700@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; ^{meenu.goyaliitr@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：q&minus ; q&minus ; Bernstein&ndash ; Schurer operators ; Rate of convergence ; Modulus of continuity ; Lipschitz type class ; Degree of approximation
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：275
• 期：Complete
• 页码：372-385
• 全文大小：2141 K

文摘

The purpose of this paper is to obtain some direct results for the Durrmeyer variant of q−$q-$Bernstein–Schurer operators for functions of one variable introduced by Acu et al. [1]. We also propose to study the bivariate extension of these operators and discuss the rate of convergence by using the modulus of continuity, the degree of approximation for the Lipschitz class of functions and the Voronovskaja type asymptotic theorem. Furthermore, we show the convergence of the operators by illustrative graphics in Maple to certain functions in both one and two dimensional cases.