The main object of this paper is to apply the method of differential subordinations in order to obtain certain properties of some subclasses of analytic functions in the unit disc involving differential subordinations. 2009 Elsevier Inc. All rights reserved.

In this paper, we obtain some second order differential subordinations of holomorphic mappings on a bounded convex balanced domain Ω in C. These results imply some first order differential subordinations of holomorphic mappings on a bounded convex balanced domain Ω in C. When Ω is the unit disc in the complex plane C, these results are just ones of Miller and Mocanu et al. about differential su...

By using the method of differential subordinations, we derive some sufficient conditions for strongly starlike functions associated with a linear operator. All these results presented here are sharp.

By applying certain integral operators to p-valent functions we define a comprehensive family of analytic functins. The subordinations properties of this family is studied, which in certain special cases yield some of the previously obtained results.

By using the method of differential subordinations, we derive certain sufficient conditions for strongly starlike functions associated with an integral operator. All these results presented here are sharp. 2000 Mathematics Subject Classification. Primary 30C45; Secondary 30A10.

Differential subordinations and superordinations results are obtained for certain meromorphic functions in the punctured unit disk which are associated with an integral operator. These results are obtained by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained

The aim of the present paper is to derive some new properties of analytic functions defined by the linear operator ), ( ) , ( z f c a Lp using differential subordinations techniques. Mathematics Subject Classification: 30C45

In this paper we establish several strong differential subordinations regarding an extended new operator obtained as a linear combination of an extended Ruscheweyh derivative and an extended new multiplier transformation. A number of interesting consequences of these strong subordination results are discussed.

* Correspondence: [email protected] Department of Mathematics, Yangzhou University, Yangzhou, 225002, PR China Full list of author information is available at the end of the article Abstract By using the method of differential subordinations, we derive certain properties of meromorphically multivalent functions. 2010 Mathematics Subject Classification: 30C45; 30C55.