In the present paper, we study a class of integral operators of probabilistic type, which are constructed by means of the generalized Gamma distribution. In particular, we discuss their approximation properties in weighted continuous function spaces and Lp-spaces, providing some estimates of the rate of convergence by means of different moduli of smoothness as well as an asymptotic formula. The paper concludes with some illustrative examples.
On the approximation properties of generalized Gamma-type operators in several function spaces / Cappelletti Montano, Mirella; Leonessa, Vita; Travaglini, Arianna. - In: ANNALS OF FUNCTIONAL ANALYSIS. - ISSN 2008-8752. - ELETTRONICO. - 16:(2025), pp. 59.1-59.22. [10.1007/s43034-025-00453-1]
On the approximation properties of generalized Gamma-type operators in several function spaces
Leonessa, Vita;Travaglini, Arianna
2025
Abstract
In the present paper, we study a class of integral operators of probabilistic type, which are constructed by means of the generalized Gamma distribution. In particular, we discuss their approximation properties in weighted continuous function spaces and Lp-spaces, providing some estimates of the rate of convergence by means of different moduli of smoothness as well as an asymptotic formula. The paper concludes with some illustrative examples.
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