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

Let S*c (α, σ,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 + a2z^2 + a3z^3 + · · · + anz^n + · · · = z + Σ Pn=2 anz^n and normalized with f (0) = 0and f (0) − 1 = 0 and satisfy (eiα zf (z)/g(z) − σ − i sin α) 1/ tασ 1+Az /1+Bz , −1 ≤ B A ≤ 1, z (element of) E where g (z) = f(z)+f(¯z)/ 2 , tασ = cosα −σ, cos α − σ 0, 0 ≤ σ 1 and |α| π/ 2 . In this paper, we determine the sharp upper bound of the functional˛˛a2a4 − a23 ˛˛ for this class of functions. The results generalize some known existing results in the literature.