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Zbl 1211.41004
Gupta, Vijay; Kim, Taekyun
On the rate of approximation by $q$ modified beta operators. (English)
[J] J. Math. Anal. Appl. 377, No. 2, 471-480 (2011). ISSN 0022-247X

The authors propose the $q$ analogue of the modified Beta operators. They apply $q$-derivatives to obtain the central moments of the discrete $q$-Beta operators. A direct result in terms of modulus of continuity for the $q$-operators is also established. They have also used the properties of $q$-integral to establish the recurrence formula for the moments of $q$-modified Beta operators and an asymptotic formula.
[Vijay Gupta (New Delhi)]

MSC 2000:: *41A25 Degree of approximation, etc.
41A36 Approximation by positive operators

Keywords: linear positive operators; modified beta operators; modulus of continuity; $q$-integers; $q$-beta functions; $q$-derivatives; $q$-integrals; rate of approximation

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