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International Journal of Mathematics and Mathematical Sciences
Volume 2008, Article ID 905635, 11 pages
Research Article

Matrix Transformations and Disk of Convergence in Interpolation Processes

Department of Mathematics, Pennsylvania State University, Shenango Campus, 147 Shenango Avenue, Sharon, PA 16146, USA

Received 23 May 2008; Accepted 22 July 2008

Academic Editor: Huseyin Bor

Copyright © 2008 Chikkanna R. Selvaraj and Suguna Selvaraj. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let 𝐴 𝜌 denote the set of functions analytic in | 𝑧 | < 𝜌 but not on | 𝑧 | = 𝜌 ( 1 < 𝜌 < ) . Walsh proved that the difference of the Lagrange polynomial interpolant of 𝑓 ( 𝑧 ) 𝐴 𝜌 and the partial sum of the Taylor polynomial of 𝑓 converges to zero on a larger set than the domain of definition of 𝑓 . In 1980, Cavaretta et al. have studied the extension of Lagrange interpolation, Hermite interpolation, and Hermite-Birkhoff interpolation processes in a similar manner. In this paper, we apply a certain matrix transformation on the sequences of operators given in the above-mentioned interpolation processes to prove the convergence in larger disks.