A note on Briot-Bouquet-Bernoulli differential subordination

Kanas, Stanisława ; Kowalczyk, Joanna

Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 2, pp. 339-347.

Résumé

Let $p, q$ be analytic functions in the unit disk $\Cal U$. For $\alpha \in [0,1)$ the authors consider the differential subordination and the differential equation of the Briot-Bouquet type: $$ p^{1-\alpha}(z)+\frac{zp'(z)}{\delta p^{\alpha}(z) + \lambda p(z)}\prec h(z), \quad z\in \Cal U, $$ $$ q^{1-\alpha}(z)+\frac{nzq'(z)}{\delta q^{\alpha}(z)+\lambda q(z)} = h(z),\quad z\in \Cal U, $$ with $p(0) =q(0) =h(0)=1$. The aim of the paper is to find the dominant and the best dominant of the above subordination. In addition, the authors give some particular cases of the main result obtained for appropriate choices of functions $h$.

Détail

Classification : 30C35, 30C45, 30C80, 34A25
Keywords: differential subordinations; Briot-Bouquet-Bernoulli differential sub\-or\-di\-na\-tion