Approximation Properties of Two-Dimensionalq-Bernstein-Chlodowsky-Durrmeyer Operators

Abstract

This article deals with the Durrmeyer-type generalization of the q-Bernstein-Chlodowsky operators on a rectangular domain (which were introduced by Büyükyazıcı [2]). We obtain the Korovkin-type approximation properties and the rates of convergence of this generalization using the means of the modulus of continuity and using the K -functional of Peetre. Further, we establish the weighted approximation properties for these operators.

The Approximation of Bivariate Blending Variant Szász Operators Based Brenke Type Polynomials

“…In the last few decades the convergence estimation for linear positive operators is an active area of research amongst researchers. Several new operators have been introduced and their convergence behavior has been discussed (see [5][6][7][8]). In [9,10] authors introduced a bivariate blending variant of the Szász type operators and studied local approximation properties for these operators.…”

Results on Bivariate Modified (p, q)-Bernstein Type Operators

“…For example, q-Bernstein polynomials were defined [2] by Phillips in 1997. Some generalizations of Bernstein operators using q-integers can be found in [3][4][5][6]. Then q-calculus is extended to (𝑝, 𝑞)-calculus in approximation theory.…”

Approximation by Sequence of Operators Including Dunkl–Appell Polynomials

“…Because of the importance of q -Bernstein polynomials in many fields of application such as pattern recognition and computer aided geometry design, these kinds of polynomials have been extensively studied in the literature. There are many papers and several books published on q -Bernstein polynomials ( [4], [5], [6], [7], [8]).…”