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On a generalization of Kantorovich operators on simplices and hypercubes

On a generalization of Kantorovich operators on simplices and hypercubes 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 ≥ 1). These operators represent a natural generalization to the multidimensional setting of the ones introduced in (Altomare and Leonessa, Mediterr. J. Math. 3: 363–382, 2006) 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

On a generalization of Kantorovich operators on simplices and hypercubes

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References (8)

Publisher
de Gruyter
Copyright
Copyright © 2010 by the
ISSN
1867-1152
eISSN
1869-6090
DOI
10.1515/apam.2010.024
Publisher site
See Article on Publisher Site

Abstract

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 ≥ 1). These operators represent a natural generalization to the multidimensional setting of the ones introduced in (Altomare and Leonessa, Mediterr. J. Math. 3: 363–382, 2006) 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.

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Sep 1, 2010

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