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RESEARCH PRODUCT

Approximation properties of λ-Kantorovich operators

Daniel Florin SofoneaNesibe ManavAna Maria Acu

subject

Pure mathematicsBernstein operatorModulus of smoothnessResearchApplied Mathematicslcsh:Mathematics010102 general mathematicsType (model theory)Rate of convergenceLambdalcsh:QA1-93901 natural sciences010101 applied mathematicsRate of convergenceVoronovskaja theorem41A10Discrete Mathematics and CombinatoricsKantorovich operators0101 mathematics41A2541A36AnalysisMathematics

description

In the present paper, we study a new type of Bernstein operators depending on the parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda\in[-1,1]$\end{document}λ∈[−1,1]. The Kantorovich modification of these sequences of linear positive operators will be considered. A quantitative Voronovskaja type theorem by means of Ditzian–Totik modulus of smoothness is proved. Also, a Grüss–Voronovskaja type theorem for λ-Kantorovich operators is provided. Some numerical examples which show the relevance of the results are given.

yearjournalcountryeditionlanguage
2018-08-01Journal of Inequalities and Applications
10.1186/s13660-018-1795-7http://link.springer.com/article/10.1186/s13660-018-1795-7