GENERALIZED HERMITE-FEJÉR INTERPOLATION BY THE FUNCTION WITH NON-UNIFORM
NODES ON THE UNIT CIRCLE
By
Swarnima Bahadur and Sameera Iqram
Department of Mathematics & Astronomy, University of Lucknow, Lucknow-226007, Uttar Pradesh, India
Email: swarnimabahadur@ymail.com, sameeraiqram787@gmail.com
(Received: October 03, 2022; In format : October 07, 2022; Revised : Novermber 18, 2022; Accepted : Novermber 20, 2022)
DOI: https://doi.org/10.58250/jnanabha.2022.52231
Abstract
In this research paper, we consider generalized Hermite-Fejer interpolation on the nodes, which are obtained by vertically projected zeros of the (1 + x)P(α,β)n (x) on the unit circle, where P(α,β)n (x) stands for Jacobi polynomial. Explicitly representing the interpolatory polynomial as well as establishment of convergence theorem are the key highlights of this paper.
2020 Mathematical Sciences Classification: 65D05, 41A10, 41A05, 40A30, 30E10.
Keywords and Phrases: Jacobi Polynomial, Rate of Convergence, Hermite-Fejér Interpolation.