Approximation properties of λ-Kantorovich operators

作者：Acu AM, Manav N, Sofonea DF · 发表于：Journal of inequalities and applications · 年份：2018 · DOI：10.1186/s13660-018-1795-7

In the present paper, we study a new type of Bernstein operators depending on the parameter 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.