Abstract
In this paper, we have studied an almost quasi Hermite-Fejer-type interpolation in rational spaces. A Radau type quadrature formula has also been obtained for the same.
Highlights
Hermite Fejer and Quasi-Hermite-Fejer-type interpolation processes has been a subject of interest for several mathematicians
In almost all the cases the interpolatory polynomials are considered on the nodes which are the zeros of certain classical orthogonal polynomials
The main idea of the present paper is to construct a rational interpolation process and its corresponding quadrature formula with prescribed nodes based on the Chebyshev Markov fractions
Summary
Hermite Fejer and Quasi-Hermite-Fejer-type interpolation processes has been a subject of interest for several mathematicians. The main idea of the present paper is to construct a rational interpolation process and its corresponding quadrature formula with prescribed nodes based on the Chebyshev Markov fractions. Based on the ideas of [6] and using method that was different from that of [4], Rouba et al ( [5], [8]) revisited the rational interpolation functions of Hermite-Fejer-type They proved the uniform convergence of the interpolation process for the function f ∈ C[−1, 1] and obtained explicitly its corresponding Lobatto type quadrature formula. We have considered an almost quasi-Hermite-Fejer-type interpolation process on the zeros of the rational Chebyshev-Markov sine fraction on the semi closed interval A Radau type quadrature formula corresponding to the interpolation process has been obtained
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More From: International Journal of Analysis and Applications
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