GBS operators of bivariate Bernstein‐Durrmeyer–type on a triangle

Abstract

The purpose of the present paper is to define the GBS (Generalized Boolean Sum) operators associated with the two‐dimensional Bernstein‐Durrmeyer operators introduced by Zhou 1992 and study its approximation properties. Furthermore, we show the convergence and comparison of convergence with the GBS of the Bernstein‐Kantorovich operators proposed by Deshwal et al 2017 by numerical examples and illustrations.

Some approximation properties by a class of bivariate operators

“…Let . The GBS operator associated to a linear operator is defined as During time some researchers constructed and studied different type of GBS operators as we can see for example papers in Bărbosu et al, Kajla and Miclăuş, and Ruchi et al…”

“…exists and is finite. During time some researchers constructed and studied different type of GBS operators as we can see for example papers in Bȃrbosu et al, 18 Kajla and Miclȃuş, 19 and Ruchi et al 20 Let f ∈ C b (I 2 ). The GBS operator G M n,m associated to B M n,m can be introduced as follows…”

Degree of approximation for bivariate extension of blending type q -Durrmeyer operators based on Pólya distribution

“…Thereafter, many authors studied new classes of q-generalized operators and established many interesting properties. Some important results in this direction are mention in the papers [1,2,4,5,7,9,11,13,14,16,17]. Details regarding the definitions and notions of q-calculus can be found at [3].…”

On the Approximation Properties of q − Analogue Bivariate λ -Bernstein Type Operators

“…Many authors also considered the univariate and bivariate positive linear operators and studied their approximation behavior; we refer the reader to articles (cf. [8][9][10][11][12][13][14][15][16][17]) and references therein. Now, we give some basic definitions based on the q -calculus [18], which are used in this paper.…”