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Volume 31, Issue 1
Convergence of the $q$ Analogue of Szász-Beta-Stancu Operators

Y. Xu & X. M. Hu

DOI: 10.4208/ata.2015.v31.n1.4

Anal. Theory Appl., 31 (2015), pp. 45-57.

Published online: 2017-01

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  • Abstract

In the present paper, we propose the $q$ analogue of Szász-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergence and weighted approximation properties of the $q$ operators. Voronovskaja type theorem is also obtained. Our results generalize and supplement some convergence results of the $q$-Szász-Beta operators, thus they improve the existing results.

  • Keywords

$q$-Szász-Beta operators, $q$-analogues, modulus of smoothness, stancu, weighted approximation.

  • AMS Subject Headings

41A25, 41A35, 41A36

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-31-45, author = {Y. Xu and X. M. Hu}, title = {Convergence of the $q$ Analogue of Szász-Beta-Stancu Operators}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {1}, pages = {45--57}, abstract = {

In the present paper, we propose the $q$ analogue of Szász-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergence and weighted approximation properties of the $q$ operators. Voronovskaja type theorem is also obtained. Our results generalize and supplement some convergence results of the $q$-Szász-Beta operators, thus they improve the existing results.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n1.4}, url = {http://global-sci.org/intro/article_detail/ata/4621.html} }
TY - JOUR T1 - Convergence of the $q$ Analogue of Szász-Beta-Stancu Operators AU - Y. Xu & X. M. Hu JO - Analysis in Theory and Applications VL - 1 SP - 45 EP - 57 PY - 2017 DA - 2017/01 SN - 31 DO - http://doi.org/10.4208/ata.2015.v31.n1.4 UR - https://global-sci.org/intro/article_detail/ata/4621.html KW - $q$-Szász-Beta operators, $q$-analogues, modulus of smoothness, stancu, weighted approximation. AB -

In the present paper, we propose the $q$ analogue of Szász-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergence and weighted approximation properties of the $q$ operators. Voronovskaja type theorem is also obtained. Our results generalize and supplement some convergence results of the $q$-Szász-Beta operators, thus they improve the existing results.

Y. Xu and X. M. Hu. (2017). Convergence of the $q$ Analogue of Szász-Beta-Stancu Operators. Analysis in Theory and Applications. 31 (1). 45-57. doi:10.4208/ata.2015.v31.n1.4
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