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On differential sandwich theorems of analytic functions defined by certain generalized linear operator

Seoudy T. M., Aouf M. K.

Journal of Mathematics and Applications

2014

Vol. 37

97--109

In this paper, we obtain some applications of first order differential subordination and superordination results involving certain linear operator and other linear operators for certain normalized analytic functions. Some of our results improve and generalize previously known results.

Preserving subordination and superordination results of generalized Srivastava-Attiya operator

Aouf M. K., Mostafa A. O., Shahin A. M., Madian S. M.

Journal of Mathematics and Applications

2013

Vol. 36

17--26

In this paper, we obtain some subordination and superordination-preserving results of the generalized Srivastava-Attyia operator. Sandwich-type result is also obtained.

On some classes of meromorphic functions defined by subordination and superordination

Totoi A.

Opuscula Mathematica

2011

Vol. 31, no. 4

651-668

Let p ∈ N* and β,γ ∈ C with β,≠ 0 and let ∑p denote the class of meromorphic functions of the form g(z) = α-p/zp + α0 + α1z + …, z ∈ U, α-p ≠ 0. We consider the integral operator Jp,β,γ : Kp,β,γ: ⊂ ∑p → ∑p defined by [formula]. We introduce some new subclasses of the class ∑p, associated with subordination and superordination, such that, in some particular cases, these new subclasses are the well-known classes of meromorphic starlike functions and we study the properties of these subclasses with respect to the operator Jp,β,γ.

Sandwich theorems for certain subclasses of analytic functions defined by family of linear operators

Mostafa A. O., Aouf M. K.

Journal of Applied Analysis

2009

Vol. 15, nr 2

269-280

In this paper, we obtain some applications of first order differential subordination and superordination results involving Dziok-Srivastava operator and other linear operators for certain normalized analytic functions in the open unit disk. The results, which are presented in this paper, have relevant connections with various previous results.