GBS operators of Bernstein-Schurer-Kantorovich type based on q-integers

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• 作者：Manjari Sidharth ; ^a ; ^{manjarisidharth93@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}
• 关键词：q-Bernstein&ndash ; Schurer&ndash ; Kantorovich operators ; Partial moduli of continuity ; B-continuous ; B-differentiable ; GBS operators ; Modulus of smoothness
• 刊名：Applied Mathematics and Computation
• 出版年：2015
• 出版时间：15 October 2015
• 年：2015
• 卷：269
• 期：Complete
• 页码：558-568
• 全文大小：339 K

文摘

Agrawal et al. (2015) constructed a bivariate generalization of a new kind of Kantorovich-type q-Bernstein–Schurer operators and studied a Voronovskaja type theorem and the rate of convergence in terms of the Lipschitz class function and the complete modulus of continuity. The concern of this paper is to obtain the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and the Peetre’s K-functional. Finally, we construct the GBS (Generalized Boolean Sum) operators of bivariate q-Bernstein–Schurer–Kantorovich type and estimate the rate of convergence for these operators with the help of mixed modulus of smoothness.