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On a generalization of Kantorovich operators on simplices and hypercubes
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Francesco Altomare
Veröffentlicht/Copyright:
21. April 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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Artikel in diesem Heft
- 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
Schlagwörter für diesen Artikel
N-dimensional hypercube;
N-dimensional simplex;
positive approximation process;
Kantorovich operator;
moduli of smoothness
Artikel in diesem Heft
- 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
