International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 905635, 11 pages
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 denote the set of functions analytic in but not on . Walsh proved that the difference of the Lagrange polynomial
interpolant of and the partial sum of the Taylor polynomial
of converges to zero on a larger set than the domain of definition of . 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.