Perturbed Bernstein-type operators
Ana Maria Acu, Heiner Gonska
TL;DR
This paper introduces modified Bernstein-type operators, improves existing results, and provides direct estimates and asymptotic formulas, enhancing the understanding of their approximation properties.
Contribution
It presents new modifications of classical Bernstein-type operators with improved results and detailed asymptotic analysis.
Findings
Improved direct estimates using modulus of continuity.
Established asymptotic formulas for the modified operators.
Enhanced approximation properties of the new operators.
Abstract
The present paper deals with modifications of Bernstein, Kantorovich, Durrmeyer and genuine Bernstein-Durrmeyer operators. Some previous results are improved in this study. Direct estimates for these operators by means of the first and second modulus of continuity are given. Also the asymptotic formulas for the new operators are proved.
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