Briot-Bouquet differential superordinations and sandwich theorems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:329

Article

Miller, Sanford S. ; Mocanu, Petru T.

关键词: differential subordination;    differential superordination;    Briot-Bouquet;    univalent;    convex;    starlike;   

DOI  :  10.1016/j.jmaa.2006.05.080

来源: Elsevier

【 摘 要 】

Briot-Bouquet differential subordinations play a prominent role in the theory of differential subordinations. In this article we consider the dual problem of Briot-Bouquet differential superordinations. Let beta and gamma be complex numbers, and let Omega be any set in the complex plane C. The function p analytic in the unit disk U is said to be a solution of the Briot-Bouquet differential superordination if Omega subset of {p(z) + zp'(z)/beta p(z) + gamma vertical bar z is an element of U} The authors determine properties of functions p satisfying this differential superordination and also some generalized versions of it. In addition, for sets Omega(1) and Omega(2) in the complex plane the authors determine properties of functions p satisfying a Briot-Bouquet sandwich of the form Omega(1) subset of {p(z) + zp'(z)/beta p(z) + gamma vertical bar z is an element of U} subset of Omega(2). Generalizations of this result are also considered. (c) 2006 Elsevier Inc. All rights reserved.

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