The sharp bounds of the second and third Hankel determinants for the class SL^*

Abstract

The aim of the present paper is to obtain the sharp bounds of the Hankel determinants H_2(3) and H_3(1) for the well known class SL^* of starlike functions associated with the right lemniscate of Bernoulli. Further for n=3, we find the sharp bound of the Zalcman functional for the class SL^*. In addition, a couple of interesting results of SL^* is appended at the end.