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

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Zeng X.-M., Gupta V.

Open Mathematics

2009

tom 7

nr 3

550-557

The pointwise approximation properties of the Bézier variant of the MKZ-Kantorovich operators $$ \hat M_{n,\alpha } (f,x) $$ 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 $$ \hat M_{n,\alpha } (f,x) $$ 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 $$ \hat M_{n,\alpha } (f,x) $$ for the case 0 < α < 1. In the end we propose the q-analogue of MKZK operators.

Ograniczanie wyników

1 Open Mathematics

1 Gupta V.

1 Zeng X.-M.

1 2009

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