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Acta Mathematica Hungarica

, Volume 139, Issue 3, pp 255–275 | Cite as

Approximation of some Feller semigroups associated with a modification of Szász–Mirakjan–Kantorovich operators

  • Mirella Cappelletti MontanoEmail author
  • Vita Leonessa
Article

Abstract

We deepen the study of a sequence (C n ) n≧1 of positive linear operators, first introduced in [4], that generalize the classical Szász–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 C 0-semigroups generated by the second order differential operator
$$V_l(u)(x)=xu''(x)+\frac{l}{2} u'(x)\quad (x \geqq 0,\ l \in [0, 2]) $$
on suitable domains of continuous or integrable functions may be approximated by means of iterates of the C n ’s.

Key words and phrases

positive approximation process Szász–Mirakjan–Kantorovich operator asymptotic formula degenerate second order differential operator iterate of operators Feller semigroup approximation of semigroups 

Mathematics Subject Classification

47D06 47F05 35A35 41A36 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di Bari “A. Moro”BariItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità degli Studi della BasilicataPotenzaItaly

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