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

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Summary

Introduction

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

Preliminaries
Almost Quasi-Hermite-Fejer-type interpolation
Explicit Representation of the Fundamental Functions
Radau-type quadrature formula

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