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Volume 47, Issue 4
Properties of Convergence for a Class of Generalized $q$-Gamma Operators.

Qing-Bo Cai

DOI: 10.4208/jms.v47n4.14.03

J. Math. Study, 47 (2014), pp. 388-395.

Published online: 2014-12

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  • Abstract

In this paper, a generalization of $q$-Gamma operators based on the concept of $q$-integer is introduced. We investigate the moments and central moments of the operators by computation, obtain a local approximation theorem and get the pointwise convergence rate theorem and also obtain a weighted approximation theorem. Finally, a Voronovskaya type asymptotic formula was given.

  • Keywords

$q$-integer, $q$-Gamma operators, weighted approximation, modulus of continuity.

  • AMS Subject Headings

41A10, 41A25, 41A36

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

qbcai@126.com (Qing-Bo Cai)

  • BibTex
  • RIS
  • TXT
@Article{JMS-47-388, author = {Cai , Qing-Bo}, title = {Properties of Convergence for a Class of Generalized $q$-Gamma Operators. }, journal = {Journal of Mathematical Study}, year = {2014}, volume = {47}, number = {4}, pages = {388--395}, abstract = {

In this paper, a generalization of $q$-Gamma operators based on the concept of $q$-integer is introduced. We investigate the moments and central moments of the operators by computation, obtain a local approximation theorem and get the pointwise convergence rate theorem and also obtain a weighted approximation theorem. Finally, a Voronovskaya type asymptotic formula was given.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v47n4.14.03}, url = {http://global-sci.org/intro/article_detail/jms/9964.html} }
TY - JOUR T1 - Properties of Convergence for a Class of Generalized $q$-Gamma Operators. AU - Cai , Qing-Bo JO - Journal of Mathematical Study VL - 4 SP - 388 EP - 395 PY - 2014 DA - 2014/12 SN - 47 DO - http://doi.org/10.4208/jms.v47n4.14.03 UR - https://global-sci.org/intro/article_detail/jms/9964.html KW - $q$-integer, $q$-Gamma operators, weighted approximation, modulus of continuity. AB -

In this paper, a generalization of $q$-Gamma operators based on the concept of $q$-integer is introduced. We investigate the moments and central moments of the operators by computation, obtain a local approximation theorem and get the pointwise convergence rate theorem and also obtain a weighted approximation theorem. Finally, a Voronovskaya type asymptotic formula was given.

Qing-Bo Cai. (2019). Properties of Convergence for a Class of Generalized $q$-Gamma Operators. . Journal of Mathematical Study. 47 (4). 388-395. doi:10.4208/jms.v47n4.14.03
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