Title

Convergence of generalized singular integrals to the unit, univariate case

Abstract

In a recent paper, the second author (see [2]) studied the degree of uniform approximation to the unit in terms of uniform moduli of smoothness, by the Jackson-type generalizations of Picard and of Gauss-Weierstrass singular integrals. In this paper we consider the Lp-approximation, (1 ≤ p < +∞) by the above singular integrals in terms of the Lp-moduli of smoothness, and both uniform and Lp-approximation (in terms of the corresponding moduli of smoothness) by Jackson-type generalizations of the Poisson-Cauchy singular integrals.

Publication Title

Mathematical Inequalities and Applications

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