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A note on the rate of convergence for Chebyshev-Lobatto and Radau systems

Elías Berriochoa, Alicia Cachafeiro, Jaime Díaz, Eduardo Martínez (2016)

Open Mathematics

This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.

Approximation and shape preserving properties of the nonlinear Bleimann-Butzer-Hahn operators of max-product kind

Barnabás Bede, Lucian Coroianu, Sorin G. Gal (2010)

Commentationes Mathematicae Universitatis Carolinae

Starting from the study of the Shepard nonlinear operator of max-prod type in (Bede, Nobuhara et al., 2006, 2008), in the book (Gal, 2008), Open Problem 5.5.4, pp. 324–326, the Bleimann-Butzer-Hahn max-prod type operator is introduced and the question of the approximation order by this operator is raised. In this paper firstly we obtain an upper estimate of the approximation error of the form ω 1 ( f ; ( 1 + x ) 3 2 x / n ) . A consequence of this result is that for each compact subinterval [ 0 , a ] , with arbitrary a > 0 , the order of uniform...

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