The starlikeness of analytic functions of Koebe type

We investigate the new class Hb(α,β)Hb(α,β) of analytic functions with Koebe type. The subordination, superordination, best dominant result for that class was obtain. And by making use of Jack’s Lemma as well as several differential and other inequalities, the authors derive sufficient conditions for starlikeness of the class Hb(α,β)Hb(α,β) of nn-fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in earlier works are also indicated.