In present paper, we use fractional integral and Wanas differential operator to obtain some subordination superordination results associated with Hadamard product for univalent analytic functions defined in the open unit disk. These are applied sandwich results. Our extend corresponding previously known

We investigate the new class H b (α, β) of analytic functions with Koebe type. The subordination, superordination, best dominant result for that class was obtain. And by making use of Jack's Lemma as well as several differential and other inequalities, the authors derive sufficient conditions for starlikeness of the class H b (α, β) of n-fold symmetric analytic functions of Koebe type. Relevant...

Extension of two known facts concerning subordination is made. The first fact is that, in subordination of 1-dimensional Brownian motion with drift, selfdecomposability is inherited from subordinator to subordinated. This is extended to subordination of cone-parameter convolution semigroups. The second fact is that, in subordination of strictly stable cone-parameter convolution semigroups on R,...

To obtain the main result of present paper we use technique differential subordination. As special cases our result, sufficient conditions for $f\in\mathcal A$ to be $\phi-$like, starlike and close-to-convex in a parabolic region.

It has been shown by Voiculescu and Biane that the analytic subordination property holds for free additive and multiplicative convolutions. In this paper, we present an operatorial approach to subordination for free multiplicative convolutions. This study is based on the concepts of ‘freeness with subordination’, or ‘s-free independence’, and ‘orthogonal independence’, introduced recently in th...

The results obtained by the authors in present paper refer to quantum calculus applications regarding theories of differential subordination and superordination. These are established means an operator defined as q-analogue multiplier transformation. Interesting superordination derived involving functions belonging a new class normalized analytic open unit disc U, which is investigated here usi...

Abstract: In this paper we introduce a new subclass of normalized analytic functions in the open unit disc which is defined by the Al-Oboudi differential operator. A coefficient inequality, extreme points and integral mean inequalities of a differential operator for this class are given. We investigate various subordination results for the subclass of analytic functions and obtain sufficient co...