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New Results on Rational Approximation

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Abstract

First asymptotic relations of Voronovskaya-type for rational operators of Shepard-type are shown. A positive answer in some senses to a problem on the pointwise approximation power of linear operators on equidistant nodes posed by Gavrea, Gonska and Kacsó is given. Direct and converse results, computational aspects and Grüss-type inequalities are also proved. Finally an application to images compression is discussed, showing the outperformance of such operators in some senses.

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Authors and Affiliations

  1. Istituto per le Applicazioni del Calcolo ‘M. Picone’, National Research Council of Italy, Via Pietro Castellino 111, 80131, Napoli, Italy

    Umberto Amato

  2. Dipartimento di Matematica, Università di Roma ‘La Sapienza’, Piazzale Aldo Moro 5, 00185, Rome, Italy

    Biancamaria Della Vecchia

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  1. Umberto Amato
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  2. Biancamaria Della Vecchia
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Correspondence to Biancamaria Della Vecchia.

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Dedicated to the memory of Prof. D.D. Stancu

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Amato, U., Della Vecchia, B. New Results on Rational Approximation. Results. Math. 67, 345–364 (2015). https://doi.org/10.1007/s00025-014-0420-4

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