Some Bounds of Radius of Convexity of a Class of Analytic Functions

Abstract

Let $G\left( {\alpha ,\delta } \right)$ denote the class of function $f$, $f\left( 0 \right)={f}'\left( 0 \right)-1=0$ for which $Re\left\{ {e^{i\alpha }{f}'\left( z \right)} \right\}>\delta $ in $D=\left\{ {z:\left| z \right| < 1} \right\}$ where \left| \alpha \right|\le \pi and \cos \alpha < \delta $. We obtain some sharp results related to its radius of convexity. Keywords: Analytic functions; convex; and radius of convexity.