Second Hankel determinant and coefficient problems in a set of analytic functions

In this paper we consider the class of functions f analytic in the open unit disc \(|z|<1\) with the normalization \(f(0)=f'(0)-1=0\) that satisfy the condition \( zf'(z)=G(z)P(z)\) for some odd function G and some function P with positive real part and with certain restrictions on they Taylor’s coefficients. For this class we establish the bounds for the coefficients and for the Fekete-Szegö functional. Moreover, the sharp bound of the second Hankel determinant is found.