International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 5, Pages 335-344
On rational approximation in a ball in
1Department of Mathematics, Howard University, 2441 6th Street, N. W. Washington D. C 20059, USA
2Department of Mathematics, Lincoln University, 19352, PA, USA
Received 9 July 1998
Copyright © 2000 P. W. Darko et al. 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.
We study rational approximations of
elements of a special class of meromorphic functions which are
characterized by their holomorphic behavior near the origin in
balls in by means of their rational approximants. We
examine two modes of convergence for this class: almost
uniform-type convergence analogous to Montessus-type convergence
and weaker form of convergence using capacity based on the
classical Tchebychev constant. These methods enable us to
generalize and extend key results of Pommeranke and Gonchar.