Radius of exponential convexity of certain subclass of analytic functions


Varma, S. Sunil, Rosy, Thomas and Vadivelan, U.


Abstract

creative_2020_29_1_109_112_abstract

Let \mathcal{S} be the class of analytic normalized univalent functions defined on the unit disk\linebreak \Delta = \lbrace z \in \mathbb{C} : |z|<1 \rbrace and f, g be two functions in \mathcal{S} satisfying \displaystyle Re \bigg ( \frac{zf'(z)e^{\alpha f(z)}}{g(z)} \bigg ) >0 and \displaystyle\bigg | \frac{zf'(z)e^{\alpha f(z)}}{g(z)} - 1 \bigg | <1, \alpha \in \mathbb{C} \setminus \lbrace 0 \rbrace. We determine the radius of exponential convexity of f \in \mathcal{S} whenever g satisfies (i) \ Re \dfrac{g(z)}{z} >0 \ (ii) \ Re \dfrac{g(z)}{z} > 1/2.

 

 

Additional Information

Author(s)

   Vadivelan, U., Rosy, Thomas, Varma, S. Sunil