International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 2, Pages 285-295
Effectiveness of transposed inverse sets in faber regions
1Department of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria
27 Denchaway Street, Sidi Gaber, Alexandria, Egypt
Received 11 February 1982; Revised 15 August 1982
Copyright © 1983 J. A. Adepoju and M. Nassif. 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.
The effectiveness properties, in Faber regions, of the transposed inverse
of a given basic set of polynominals, are investigated in the present paper. A certain inevitable normalizing substitution, is first formulated, to be undergone by the given set to ensure the existence of the transposed inverse in the Faber region. The first main result of the present work (Theorem 2.1), on the one hand, provides a lower bound of the class of functions for which the normalized transposed inverse set is effective in the Faber region. On the other hand, the second main result (Theorem 5.2) asserts the fact that the normalized transposed inverse set of a simple set of polynomials, which is effective in a Faber region, should not necessarily be effective there.