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

Open Mathematics (2009)

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

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topXiao-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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