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

Xiao-Ming Zeng; Vijay Gupta

Open Mathematics (2009)

  • Volume: 7, Issue: 3, page 550-557
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Xiao-Ming Zeng, and Vijay Gupta. "Approximation by the Bézier variant of the MKZ-Kantorovich operators in the case α < 1." Open Mathematics 7.3 (2009): 550-557. <http://eudml.org/doc/269620>.

@article{Xiao2009,
abstract = {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.},
author = {Xiao-Ming Zeng, Vijay Gupta},
journal = {Open Mathematics},
keywords = {Bézier variant of the MKZ-Kantorovich operators; Rate of convergence; Pointwise approximation; Inequalities; Lebesgue-Stieltjes integral; rate of convergence; pointwise approximation; inequalities},
language = {eng},
number = {3},
pages = {550-557},
title = {Approximation by the Bézier variant of the MKZ-Kantorovich operators in the case α < 1},
url = {http://eudml.org/doc/269620},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Xiao-Ming Zeng
AU - Vijay Gupta
TI - Approximation by the Bézier variant of the MKZ-Kantorovich operators in the case α < 1
JO - Open Mathematics
PY - 2009
VL - 7
IS - 3
SP - 550
EP - 557
AB - 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.
LA - eng
KW - Bézier variant of the MKZ-Kantorovich operators; Rate of convergence; Pointwise approximation; Inequalities; Lebesgue-Stieltjes integral; rate of convergence; pointwise approximation; inequalities
UR - http://eudml.org/doc/269620
ER -

References

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