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 - <p style="text-align: justify;">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.</p>