In this paper we introduce and study a sequence of positive linear operators acting on suitable spaces of measurable functions on [0, +\infty[, including L^p([0, +\infty[) spaces, 1 \leq p <+\infty, and continuous function spaces with polynomial weights. These operators generalize the Sz\'{a}sz-Mirakjan-Kantorovich operators and they allow to approximate (or to reconstruct) suitable measurable functions by knowing their mean values on a sequence of subintervals of [0,+\infty[ that do not constitute a subdivision of it. We also give some estimates of the rates of convergence by means of suitable moduli of smoothness.
On a generalization of Szász-Mirakjan-Kantorovich operators
ALTOMARE, Francesco;CAPPELLETTI MONTANO, MIRELLA;
2013-01-01
Abstract
In this paper we introduce and study a sequence of positive linear operators acting on suitable spaces of measurable functions on [0, +\infty[, including L^p([0, +\infty[) spaces, 1 \leq p <+\infty, and continuous function spaces with polynomial weights. These operators generalize the Sz\'{a}sz-Mirakjan-Kantorovich operators and they allow to approximate (or to reconstruct) suitable measurable functions by knowing their mean values on a sequence of subintervals of [0,+\infty[ that do not constitute a subdivision of it. We also give some estimates of the rates of convergence by means of suitable moduli of smoothness.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
