International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 289-299
doi:10.1155/S016117128200026X
Generalizations of p-valent functions via the hadamard product
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403, Ohio, USA
Received 1 July 1981
Copyright © 1982 Anil K. Soni. 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.
Abstract
The classes of univalent prestarlike functions Rα, α≥−1, of Ruscheweyh [1] and a certain generalization of Rα were studied recently by Al-Amiri [2]. The author studies, among other things, the classes of p-valent functions R(α+p−1) where p is a positive integer and α is any integer with α+p>0. The author shows in particular that R(α+p)⊂R(α+p−1) and also obtains the radius of R(α+p) for the class R(α+p−1).