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On the generalized Picard and Gauss-Weierstrass singular integrals. (English) Zbl 1099.41012
In this paper the author gives the generalizations of the Picard and the Gauss-Weierstrass singular integral operators which are based on the so-called \(q\)-numbers and depend on \(q\)-generalization of the Euler gamma integral. Some approximation properties of these two generalized operators are established in \(L_p(\mathbb{R})\) and weighted \(L_{p,w}(\mathbb{R})\) spaces.

MSC:
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
41A25 Rate of convergence, degree of approximation
41A35 Approximation by operators (in particular, by integral operators)
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