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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)