STRONG DIFFERENTIAL SUBORDINATION AND APPLICATIONS TO UNIVALENCY CONDITIONS

Title & Authors
STRONG DIFFERENTIAL SUBORDINATION AND APPLICATIONS TO UNIVALENCY CONDITIONS
Antonino Jose- A.;

Abstract
For the Briot-Bouquet differential equations of the form given in [1] $\small{{{\mu}(z)+\frac {z{\mu}$ we can reduce them to $\small{{{\mu}(z)+F(z)\frac {v$ where $\small{v(z)=\alpha{\mu}(z)+\beta,\;h(z)={\alpha}g(z)+\beta\;and\;F(z)=f(z)/f$. In this paper we are going to give conditions in order that if u and v satisfy, respectively, the equations (1) $\small{{{\mu}(z)+F(z)\frac {v$, $\small{{{\mu}(z)+G(z)\frac {v$ with certain conditions on the functions F and G applying the concept of strong subordination $\small{g\;\prec\;\prec\;h}$ given in [2] by the author, implies that $\small{v\;\prec\;{\mu},\;where\;\prec}$ indicates subordination.
Keywords
differential equation;subordination;convex function;starlike function;
Language
English
Cited by
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Korean Journal of Mathematics, 2015. vol.23. 4, pp.503-519
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