@article{Güngör2025, 
author = {Şule Yüksel Güngör},
title = {Approximation properties of a moment-based modification of Bernstein operators},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {21820-21834},
keywords = {Bernstein operators, rate of convergence, modulus of continuity, Voronovskaja-type theorem},
url = {https://www.sciopen.com/article/10.3934/math.2025970},
doi = {10.3934/math.2025970},
abstract = {In this paper, a moment-based modification of the classical Bernstein operators is introduced. The proposed operators incorporate both a domain transformation and an adjustment by the second central moment to improve the approximation properties. We investigate their convergence behavior using tools such as the Lipschitz class and Peetre's    κ  −functional. Quantitative estimates are established based on the classical and second-order modulus of continuity. Furthermore, a Voronovskaja-type theorem is provided to analyze the asymptotic behavior. Theoretical results are supported by numerical examples and graphical illustrations that demonstrate the effectiveness of the operators.}
}