Second Hankel Determinant for a Class of Analytic Functions Defined by Fractional Derivative

Also let S, S∗ β , CV β , and K denote, respectively, the subclasses of A0 consisting of functions which are univalent, starlike of order β, convex of order β cf. 1 , and close-to-convex cf. 2 in U. In particular, S∗ 0 S∗ and CV 0 CV are the familiar classes of starlike and convex functions in U cf. 2 . Given f and g inA, the function f is said to be subordinate to g in U if there exits a functionω ∈ A satisfying the conditions of the Schwarz Lemma such that f z g ω z , z ∈ U . We denote the subordination by