In this paper we introduce and study two new sequences of positive linear operators acting on the space of all Lebesgue integrable functions defined, respectively, on the $N$-dimensional hypercube and on the $N$-dimensional simplex ($N \geq 1$). These operators represent a natural generalization to the multidimensional setting of the ones introduced in \cite{AltomareLeonessaCn1} and, in a particular case, they turn into the multidimensional Kantorovich operators on these frameworks. We study the approximation properties of such operators with respect both to the sup-norm and to the $L^p$-norm and we give some estimates of their rate of convergence by means of certain moduli of smoothness.
On a generelization of Kantorovich operators on hypercubes and simplices
ALTOMARE, Francesco;CAPPELLETTI MONTANO, MIRELLA;
2010-01-01
Abstract
In this paper we introduce and study two new sequences of positive linear operators acting on the space of all Lebesgue integrable functions defined, respectively, on the $N$-dimensional hypercube and on the $N$-dimensional simplex ($N \geq 1$). These operators represent a natural generalization to the multidimensional setting of the ones introduced in \cite{AltomareLeonessaCn1} and, in a particular case, they turn into the multidimensional Kantorovich operators on these frameworks. We study the approximation properties of such operators with respect both to the sup-norm and to the $L^p$-norm and we give some estimates of their rate of convergence by means of certain moduli of smoothness.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
