Quantitative estimates for Jain-Kantorovich operators

Abstract

QUANTITATIVE ESTIMATES FOR JAIN-KANTOROVICH OPERATORS EMRE DEN · IZAbstract. By using given arbitrary sequences, n > 0, n 2 N with the property that limn!1n n = 0 and limn!1 n = 0, we give a Kantorovich type generalization of Jain operator based on the a Poisson disrtibition. Fristly we give the quantitative Voronovskaya type theorem. Then we also obtain the Grüss Voronovskaya type theorem in quantitative form .We show that they have an arbitrary good order of weighted approximation.

On bivariate Jain operators

“…Özarslan [20] studied Stancu type Jain operators and constructed a modification of them so that the modified operators preserve linear functions and provide a better error estimation than the Jain operators and obtained global results in a certain subspace of C[0, ∞), whereas Jain operators don't satisfy. Deniz [8] provided some quantitative estimates for Kantorovich generalization of Jain operators. For a detailed overview concerning Jain operators, we refer to Agratini's paper [3].…”