Convergence of the $q$ Analogue of Szász-Beta-Stancu Operators

Convergence of the $q$ Analogue of Szász-Beta-Stancu Operators

Year:    2015

Analysis in Theory and Applications, Vol. 31 (2015), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2015.v31.n1.4

Analysis in Theory and Applications, Vol. 31 (2015), Iss. 1 : pp. 45–57

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

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