Modified ρ-Bernstein Operators for Functions of Two Variables. (4th July 2021)

• Record Type: Journal Article
• Authors: Agrawal, P. N.; Kajla, Arun; Kumar, Dharmendra
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 9(2021)
• Page Start: 1073
• Page End: 1095
• Publication Date: 2021-07-04
• Subjects: Grüss-Voronovskaya-type theorem -- Lipschitz class; 41A10 -- 41A25 -- 41A36 -- 41A63; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1931311
• Languages: English
• ISSNs: 0163-0563

Abstract

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.