Approximation Degree of Bivariate Generalized λ-Bernstein - Kantorovich Type Operators. (26th August 2022)

• Record Type: Journal Article
• Authors: Agrawal, Purshottam Narain; Baxhaku, Behar; Singh, Sompal
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 12(2022)
• Page Start: 1484
• Page End: 1509
• Publication Date: 2022-08-26
• Subjects: Approximation by positive operators -- rate of convergence -- degree of approximation -- GBS operators -- mixed modulus of smoothness; 40A05 -- 41A25 -- 41A36; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2108443
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In the present paper, we consider a tensor product of a generalized λ -Bernstein-Kantorovich type operators and discuss its approximation properties by means of the complete and partial moduli of continuity, Lipschitz class and the Peetre's K-functional. Further, we define the GBS (Generalized Boolean Sum) operators of the above bivariate operators and investigate the convergence rate of these operators for the B o ¨ gel continuous and B o ¨ gel differentiable functions by using the mixed modulus of smoothness. Finally, we illustrate the rate of convergence and its comparison for the bivariate λ -Bernstein-Kantorovich type operators and the associated GBS operators by means of graphs and tables for certain functions by using Matlab algorithms.