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

Xiao-Ming ZengVijay Gupta — 2009

Open Mathematics

The pointwise approximation properties of the Bézier variant of the MKZ-Kantorovich operators 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 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 M ^ n , α ( f , x ) for the case 0 < α < 1. In the end we propose the q-analogue of MKZK operators....

King type modification of q -Bernstein-Schurer operators

Mei-Ying RenXiao-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...

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