MMN-1945

# On strongly starlike functions of order $(\alpha,\beta)$

*Mamoru Nunokawa*;

*Janusz Sokol*;

## Abstract

We consider the class SS*(alpha,beta) of analytic functions which
satisfy the condition
-\pi\beta/2<\arg\left\{zf'(z)/f(z)\right\}<\pi\alpha/2 for all z in
the unit disc E on the complex plane, where 0\le \alpha<1 and
0\le\beta<1. For \alpha=\beta the class SS*(alpha,beta) is equal to
the well known class SS*(beta) of strongly starlike functions of
order $\beta$. In this work we derive a sufficient condition for
analytic function to be in the class SS*(alpha,beta) strongly
starlike functions of order (\alpha,\beta).

Vol. 19 (2018), No. 1, pp. 431-437

DOI: 10.18514/MMN.2018.1945