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The Bézier variant of Kantorovich type λ-Bernstein operators

In this paper, we introduce the Bézier variant of Kantorovich type λ-Bernstein operators with parameter [Formula: see text] . We establish a global approximation theorem in terms of second order modulus of continuity and a direct approximation theorem by means of the Ditzian–Totik modulus of smoothn...

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Detalles Bibliográficos
Autor principal: Cai, Qing-Bo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5906583/
https://www.ncbi.nlm.nih.gov/pubmed/29681722
http://dx.doi.org/10.1186/s13660-018-1688-9
Descripción
Sumario:In this paper, we introduce the Bézier variant of Kantorovich type λ-Bernstein operators with parameter [Formula: see text] . We establish a global approximation theorem in terms of second order modulus of continuity and a direct approximation theorem by means of the Ditzian–Totik modulus of smoothness. Finally, we combine the Bojanic–Cheng decomposition method with some analysis techniques to derive an asymptotic estimate on the rate of convergence for some absolutely continuous functions.