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Approximation by the Bézier variant of the MKZ-Kantorovich operators in the case α < 1

Xiao-Ming Zeng; Vijay Gupta — 2009

Open Mathematics

The pointwise approximation properties of the Bézier variant of the MKZ-Kantorovich operators ${\hat{M}}_{n, α} (f, x)$ for α ≥ 1 have been studied in [Comput. Math. Appl., 39 (2000), 1-13]. The aim of this paper is to deal with the pointwise approximation of the operators ${\hat{M}}_{n, α} (f, x)$ for the other case 0 < α < 1. By means of some new techniques and new inequalities we establish an estimate formula on the rate of convergence of the operators ${\hat{M}}_{n, α} (f, x)$ for the case 0 < α < 1. In the end we propose the q-analogue of MKZK operators....

Pointwise approximation by Meyer-König and Zeller operators

Xiao-Ming Zeng; Jun-Ning Zhao — 2000

Annales Polonici Mathematici

We study the rate of pointwise convergence of Meyer-König and Zeller operators for bounded functions, and get an asymptotically optimal estimate.

Rate of approximation for the Bézier variant of Balazs-Kantorovich operators

Vijay Gupta; Xiao Ming Zeng — 2007

Mathematica Slovaca

King type modification of $q$ -Bernstein-Schurer operators

Mei-Ying Ren; Xiao-Ming Zeng — 2013

Czechoslovak Mathematical Journal

Very recently the $q$ -Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve $x^{2}$ (2003), in this paper we modify $q$ -Bernstein-Schurer operators to King type modification of $q$ -Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions $x^{2}$ and study the approximation properties of these operators. We establish a convergence theorem...