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On the rate of approximation by $q$ modified beta operators. (English) Zbl 1211.41004
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.

41A25Rate of convergence, degree of approximation
41A36Approximation by positive operators
Full Text: DOI
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