We establish that the differential subordinations of the forms p(z)+γzp′(z)≺ h(A1,B1;z) or p(z)+γzp′(z)/p(z) ≺ h(A2,B2;z) implies p(z) ≺ h(A,B;z), where γ ≥ 0 and h(A,B;z)= (1+Az)/(1+Bz) with −1≤ B <A.

In this paper, some new fuzzy differential subordinations obtained by using the integral operator Im γ : An →An introduced in [13] are obtained.

By applying the principle of differential subordination between analytic functions to a substantially general family of linear transformations, we derive an extension of the Briot-Bouquet differential subordination relations given in the monograph on the subject by Miller and Mocanu [8]. We also present a systematic discussion of various other linear transformations associated with differential...

Let A denote the class of functions f (z) which are analytic in the open unit disk and normalized by f (0) = f (0) − 1 = 0. In this paper the expression f (z)−1 f (z)/z is studied using differential subordinations and different properties of f (z) z , as well as sufficient conditions for starlikeness and univalence of f (z) ∈ A, are obtained. Also, several open problems are posed. © 2011 Elsevi...