Upper bound for third Hankel determinant of a class of analytic functions

Abstract

We establish upper bounds for second Hankel determinant, the Fekete-Szegö functional and third Hankel determinant for normalized analytic functions f ? W?(?, ?),W?(?, ?) = { f : Re ((1 ? ? + 2?)f(z)/z+ (? ? 2?)f?(z) + ?zf??(z)) > ? , where ?, ? ? 0 and ? < 1. Also, we show that these bounds reduce to the bounds of some well-known classes for particular choices of parameters ?, ? and ?.