Differential Subordination Defined by New Generalised Derivative Operator for Analytic Functions

which are analytic in the open unit disc U {z ∈ C : |z| < 1} on the complex plane C. Let S, S∗ α , C α 0 ≤ α < 1 denote the subclasses of A consisting of functions that are univalent, starlike of order α, and convex of order α in U, respectively. In particular, the classes S∗ 0 S∗ and C 0 C are the familiar classes of starlike and convex functions inU, respectively. A function f ∈ C α if Re 1 zf ′′/f ′ > α. Furthermore a function f analytic in U is said to be convex if it is univalent and f U is convex. Let H U be the class of holomorphic function in unit discU {z ∈ C : |z| < 1}. Let