Modified ρ-Bernstein Operators for Functions of Two Variables

Abstract

In this manuscript, we consider a bivariate extension of modified ρ-Bernstein operators and obtain Voronovskaya type and Grüss Voronovskaya type theorems for these operators. Further, we determine the rate of convergence of these operators in terms of the complete and partial moduli of continuity and compute an estimate of the error in terms of the Peetre’s K-functional. Also, we define the associated Generalized Boolean Sum (GBS) operators and study the rate of convergence of these operators with the aid of the mixed modulus of smoothness for the Bögel continuous and Bögel differentiable functions and the degree of approximation for the Lipschitz class of Bögel continuous functions.

Keywords:

• Grüss-Voronovskaya-type theorem
• Lipschitz class

Mathematics Subject Classification(2010)::

• 41A10
• 41A25
• 41A36
• 41A63

Acknowledgement

The authors are extremely grateful to the learned reviewers for a critical reading of the paper and making valuable comments and suggestions leading to an improvement of the paper. The third author is thankful to” The Ministry of Human Resource and Development”, India for the financial support to carry out the above work.

Data availability statement

My manuscript has no associated data.