You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Marx-Strohhäcker Differential Subordination Systems
Sanford S. Miller and Petru T. Mocanu
Proceedings of the American Mathematical Society
Vol. 99, No. 3 (Mar., 1987), pp. 527-534
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2046357
Page Count: 8
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
Let f(z) = z + a2z 2 + ⋯ be analytic in the unit disc U and let k(z) = z/(1 - z). The classic Marx-Strohhäcker result, that a convex (univalent) function f is starlike of order 1/2, can be written in terms of differential subordinations as $zf''(z)/f'(z) \prec zk''(z)/k'(z) \Rightarrow zf'(z)/f(z) \prec zk'(z)/k(z).$ The authors determine general conditions on k for which this relation holds. They also determine a different set of general conditions on k for which $zf'(z)/f(z) \prec zk'(z)/k(z) \Rightarrow f(z)/z \prec k(z)/z.$ Finally, differential subordinations with starlike superordinate functions are considered.
Proceedings of the American Mathematical Society © 1987 American Mathematical Society