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A Treatise on the Integral Calculus
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.
Advances in Pure and Applied Mathematics – de Gruyter
Published: Sep 1, 2010
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