Let Aρ 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) ∈ Aρ 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.
|Original language||English (US)|
|Journal||International Journal of Mathematics and Mathematical Sciences|
|State||Published - 2008|
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)