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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.
We prove a local saturation theorem in ordinary approximation for combinations of Durrmeyer's integral modification of Bernstein polynomials.
This is a survey of results in a particular direction of the theory of strong approximation by orthogonal series, related mostly with author's contributions to the subject.
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 . A consequence of this result is that for each compact subinterval , with arbitrary , the order of uniform...
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