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This research presents a new class of modified Bernstein operators aimed at enhancing approximation for functions of two variables.

A Novel Class of the Modified Bernstein Operators for Functions Involving Two Variables

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Novel class of Bernstein operators improves approximation in bivariate functions, suggesting enhanced convergence properties.

This research presents a new class of modified Bernstein operators aimed at enhancing approximation for functions of two variables.
Introduced a modified class of Bernstein operators incorporating squared central terms.
Investigated fundamental characteristics such as moments and behavior on test functions.
Established various approximation theorems including the Korovkin-type and Voronovskaya-type theorems.
Demonstrated improved convergence properties for smooth bivariate functions.
Derived quantitative estimates for rate of convergence with Lipschitz-type conditions.
Presented graphical and numerical examples illustrating the operators' approximation behavior.

Braha et al. (2026) studied this question.

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