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On a generalization of Kantorovich operators on simplices and hypercubes
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Francesco Altomare
Published/Copyright:
April 21, 2010
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 Lp-norm and we give some estimates of their rate of convergence by means of certain moduli of smoothness.
Keywords.: N-dimensional hypercube; N-dimensional simplex; positive approximation process; Kantorovich operator; moduli of smoothness
Received: 2009-10-17
Revised: 2010-02-08
Published Online: 2010-04-21
Published in Print: 2010-September
© de Gruyter 2010
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- The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman–Opdam theory
- β-Jacobi processes
- On Laguerre–Hahn linear functionals: the symmetric companion
- On a generalization of Kantorovich operators on simplices and hypercubes
- Existence of solutions for anisotropic quasilinear elliptic equations with variable exponent
Keywords for this article
N-dimensional hypercube;
N-dimensional simplex;
positive approximation process;
Kantorovich operator;
moduli of smoothness
Articles in the same Issue
- The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman–Opdam theory
- β-Jacobi processes
- On Laguerre–Hahn linear functionals: the symmetric companion
- On a generalization of Kantorovich operators on simplices and hypercubes
- Existence of solutions for anisotropic quasilinear elliptic equations with variable exponent
