THE SHARP BOUNDS OF THE SECOND AND THIRD HANKEL DETERMINANTS FOR THE CLASS SL

In this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Caratheodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H-3(1) and H-2(3) for the well known class SL* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: vertical bar a(3)(2) - a(5)vertical bar for the class SL* is also estimated. Further, a couple of interesting results of SL* are also discussed. (C) 2020 Mathematical Institute Slovak Academy of Sciences