Approximation Properties and$q$-Statistical Convergence of Stancu-Type Generalized Baskakov-Szász Operators

Abstract

In this article, we introduce Stancu-type modification of generalized Baskakov-Szász operators. We obtain recurrence relations to calculate moments for these new operators. We study several approximation properties and q -statistical approximation for these operators.

Approximation by q-Bernstein-Stancu-Kantorovich operators with shifted knots of real parameters

“…Since then several polynomials were generalized and studied by using q-calculus. For example related to our present theme, q-Bernstein shifted operators [20], q-Bernstein-Kantorovich operators [21], Bernstein-Kantorovich operators based on (p, q)-calculus [19], and other related operators [1], [4], [13], [25], etc.. The Bernstein operators have been extended in various forms for the purpose of approximating functions of different classes by replacing the point evaluation functionals by some integrals.…”

Statistical Convergence via q-Calculus and a Korovkin’s Type Approximation Theorem

“…For q = 1, we have a theory of quantum mechanics in a space time with constant curvature. Recently, q-calculus has been used in some matrix and non-matrix summability methods such as q-Cesàro matrix, q-Hausdorff summability and q-statistical convergence (see [2][3][4][5][6]).…”

On One- and Two-Dimensional α–Stancu–Schurer–Kantorovich Operators and Their Approximation Properties

“…In [13], the authors investigated various pointwise and uniform approximation results. Furthermore, many researchers, e.g., Kilicman et al [15], Acar et al [16], Aral et al [17], Cai et al [18,19], Çetin et al [20,21], Mohiuddine et al [22], Aslan et al [23,24], Acu et al [25], Agrawal [26], Nasiruzzaman et al [27], and Ayman-Mursaleen et al [28,29], have intensively studied α-Bernstein operators and their modifications for better approximation results. In [30][31][32] some interesting studies have been carried out.…”