Abstract
Denote S*(alpha, beta, delta) as the subclass of analytic functions f defined by f(z) = z + Sigma(infinity)(n=2) alpha(n)z(n) that satisfied Re-i delta{zf'(z) + alpha z(2)f ''(z)/f(z)} > beta in open unit disk, z is an element of D = {z:vertical bar z vertical bar < 1} for some 0 <= beta < 1, alpha >= 0 and cos delta - beta > 0. In this paper, we obtain sharp upper bound for the second Hankel determinant, vertical bar alpha(2)alpha(4) - alpha(2)(3)vertical bar for functions belonging to this subclass of functions.