Second Hankel Determinant for a Subclass of Tilted Starlike Functions with Respect to Conjugate Points

Abstract

 Let S*(alpha,delta,A,B) be the class of functions which are analytic and univalent in an open unit disc, E={z:|z|<1} of the form f(z)=z+a2z2+a3z3+---  and normalized with f(0)=0 and f'(0)-1=0 and satisfy [{exp(img.alpha).(zf'(z)/g(z))-img(sin(alpha))]/(cos(alpha)-delta) subordiate to {1+Az/1+Bz}   where cos(alpha)-delta>0, 0<=delta<1, |alpha|<pi/2 ad -1<=B<A<=1. In this paper, we determine the sharp upper bound of the functional |a2a4-a3^2|  for this class of functions. The results generalize some known existing results in the literature.