In this paper, we deepen the study of a sequence $(C_n)_{n \geq 1}$ of positive linear operators, first introduced in \cite{altomarecappellettileonessa1}, that generalize the classical Sz\'{a}sz-Mirakjan-Kantorovich operators. In particular, we present some qualitative properties and an asymptotic formula for such a sequence. Moreover, we prove that, under suitable assumptions, the Feller semigroups generated by the second order differential operator $V_c(u)(x)=xu''(x)+c u'(x)$ ($x \geq 0, c \in [0, 1])$ on suitable domains of continuous or integrable functions may be approximated by means of iterates of the $C_n$'s.
Approximation of some Feller semigroups associated with a modification of Szasz-Mirakjan-Kantorovich operators
CAPPELLETTI MONTANO, MIRELLA;
2013-01-01
Abstract
In this paper, we deepen the study of a sequence $(C_n)_{n \geq 1}$ of positive linear operators, first introduced in \cite{altomarecappellettileonessa1}, that generalize the classical Sz\'{a}sz-Mirakjan-Kantorovich operators. In particular, we present some qualitative properties and an asymptotic formula for such a sequence. Moreover, we prove that, under suitable assumptions, the Feller semigroups generated by the second order differential operator $V_c(u)(x)=xu''(x)+c u'(x)$ ($x \geq 0, c \in [0, 1])$ on suitable domains of continuous or integrable functions may be approximated by means of iterates of the $C_n$'s.File in questo prodotto:
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