Approximation in statistical sense to n-variate B-continuous functions by positive linear operators

Abstract

ABSTRACT. Our primary interest in the present paper is to prove a Korovkintype approximation theorem for sequences of positive linear operators defined on the space of all real valued n-variate B-continuous functions on a compact subset of the real n-dimensional space via statistical convergence. Also, we display an example such that our method of convergence is stronger than the usual convergence.

Approximating B-continuous functions using GBS operators of Bernstein–Schurer–Stancu type based on q-integers

“…These operators were studied by Dobrescu and Matei in [15]. Important results were obtained by Dirik and Demirici [14] regarding the approximation in statistical sense of n-variate B-continuous functions. In [17], Karakus and Demirici report results regarding the statistical r-approximation to B-continuous functions.…”

Bivariate Bernstein–Schurer–Stancu type GBS operators in $(p,q)$-analogue

“…Then, focusing on bivariate case, Bărbosu [9] introduced the generalized bivariate Stancu operators, and many researchers have worked on different operators: Örkcü [32] established the q-Szász-Mirakjan-Kantorovich bivariate operators; Mursaleen and Ahasan [28] introduced the Dunkl generalization of Stancu type q-Szász-Mirakjan-Kantorovich operators; Ostrovska [33] determined the relation between the theory of q-Bernstein polynomials and limit q-Bernstein operators. For detailed study, we refer to [3,6,11,14,20,34], and [37]. Agrawal et al [4] introduced the q-Bernstein-Schurer-Stancu operators…”

A Note On Statistical Approximation Properties of Complex q-Szász- Mirakjan Operators

“…In 2002, Gadjiev and Orhan gave some approximation results by using statistical convergence [1]. And several authors have studied in approximation theory by using statistical convergence concept (see [3], [4] and [5] [6], [7], [8], [13], [19]). Now, we give some notations on q analysis given in [16] and [21].…”