@article{Zhou2026, 
author = {Weiping Zhou and Yujie Liu and Wentao Cheng},
title = {Approximation on univariate and bivariate modified Bernstein-Kantorovich operators},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {21128-21152},
keywords = {Bernstein operators, Voronovskaya-type theorems, modulus of continuity, uniform convergence, global approximation, bivariate operators},
url = {https://www.sciopen.com/article/10.3934/math.2026858},
doi = {10.3934/math.2026858},
abstract = {In this manuscript, we introduce a new    ρ-th-order Kantorovich-type generalization of the modified Bernstein operators. First, we establish Voronovskaya-type theorems for the proposed operators. Then, we derive rates of convergence and establish global approximation theorems by means of the modulus of continuity, the        K  -functional, the Ditzian-Totik weighted moduli of smoothness and the weighted        K  -functional. Also, several numerical examples are presented to illustrate the approximation behavior using MATLAB. Finally, we construct a bivariate analog of these operators and investigate its convergence properties.}
}