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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/132715
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