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On statistical approximation properties of Kantorovich type \(q\)-Bernstein operators. (English) Zbl 1202.41017

Summary: A new Kantorovich type generalization of \(q\)-Bernstein operators is introduced with the help of some recent studies on \(q\)-calculus. Then the statistical Korovkin type approximation properties of these operators are investigated. Finally, the order of statistical approximation is examined by means of modulus of continuity and with the help of the elements of Lipschitz class.

MSC:

41A35 Approximation by operators (in particular, by integral operators)
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
40A35 Ideal and statistical convergence
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