Classical Kantorovich Operators Revisited

Abstract

The main object of this paper is to improve some of the known estimates for classical Kantorovich operators. A quantitative Voronovskaya-type result in terms of second moduli of continuity which improves some previous results is obtained. In order to explain nonmultiplicativity of the Kantorovich operators a Chebyshev-Grüss inequality is given. Two Grüss-Voronovskaya theorems for Kantorovich operators are considered as well.

Semi-discrete Gruss-Voronovskaya-type and Gruss-type estimates for Bernstein-Kantorovich polynomials

“…which is the same order which can be obtained for the classical Grüss-type estimate in terms of the least concave majorant of the modulus of continuity expressed by Theorem 4.2 in [1] for f, g ∈ C 2 [0, 1].…”

“…thus recapturing the order of approximation in the classical Grüss-Voronovskaya-type estimate given by Theorem 5.1 in [1].…”

“…Let f, g ∈ C 3 [0, 1]. Firstly, take y → x, multiply by n both members in the estimate in Theorem 2.1 and use the estimate in [1], page 849, line 7 from below…”

Multivariate weighted kantorovich operators

“…Recently, the classical Kantorovich operators received a lot of attention: see, e.g., [1], [2], [5], [6], [13]. In this paper we extend some results from [8] and [14], by introducing and studying multivariate weighted Kantorovich operators.…”

Fractional‐type integral operators and their applications to trend estimation of COVID‐19

“…We refer the interested reader in Bernstein type operators to see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] for monographs and recent modifications in the subject. In 1930, Kantorovich [18] developed an approximation process for Lebesque integrable functions on [0, 1].…”