Estimate on the second Hankel functional for functions whose derivative has a positive real part

Abstract

Denote to be the class of functions which are analytic, normalised and univalent in the open unit disc D-{z:|z|<1}. Also denote to represent the subclass of S whose derivative has a positive real part. Next, write f (z)-z+∑ a z where a is a complex constant and denote the qth Hankel determinant for f as H(n) for q>1,n>1. Our intention is to seek sharp upper bounds for H(n), however, we begin by first looking at H(2). In this paper, we give the upper bound for the second Hankel determinant for this particular class of functions.