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  • Author or Editor: B. Della Vecchia x
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Abstract  

We prove that the weighted error of approximation by the Szász-Mirakyan-type operator introduced in [1] is equivalent to the modulus of smoothness of the function. This result is analogous to previous results for Bernstein-type operators obtained by Ditzian-Ivanov and Szabados.

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Abstract  

The authors state a one-sided convergence theorem for Lagrange interpolation based on certain generalizations of Jacobi weights. In a sense the results are best possible.

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The authors establish necessary and sufficient conditions for the weightedL p convergence at given rates of Hermite interpolation of higher order based on Jacobi zeros plus the endpoints ±1. Theorems on simultaneous approximation are also proved.

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Abstract

This paper generalizes some results of L. B. Golinskii [4] on the asymptotic behaviour of reflection coefficients associated with generalized Jacobi weight functions.

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