In the present paper, we study a new type of Bernstein operators depending on the parameter . 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.
The goal of this paper is to introduce new q-Stancu-Kantorovich operators and to study some of their approximation properties. A convergence theorem using the well known Bohman-Korovkin criterion is proven and the rate of convergence involving the modulus of continuity is established. Furthermore, a Voronovskaja type theorem is also proven.
We discuss some results for q-analogues of Bernstein and Stancu operators. Moreover, a q-analogue of an operator of A. Lupaş is introduced and investigated.
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