M. K. Aouf

New subclasses of bi-univalent functions

Abstract In this paper, we introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients | a 2 | and | a 3 | for functions in these new subclasses.

On a subclass of strongly starlike functions

Abstract Let S ∗ ( q c ) , c ∈ ( 0 , 1 ] , denote the class of analytic functions f in the unit disc U normalized by f ( 0 ) = f ′ ( 0 ) − 1 = 0 and satisfying the condition | [ z f ′ ( z ) / f ( z ) ] 2 − 1 | ∣ c , z ∈ U . The relations between S ∗ ( q c ) and other classes geometrically defined are considered. The radii of convexity (starlikeness) of order α are calculated. The same problem in the class of strongly starlike functions of order β is also considered.

Majorization problem for certain class of p-valently analytic function defined by generalized fractional differintegral operator

In this paper we investigate a majorization problem for a subclass of p-valently analytic function involving a generalized fractional differintegral operator. Some useful consequences of the main result are mentioned and relevance with some of the earlier results are also pointed out.

Hadamard product of certain meromorphic starlike and convex functions

In this paper, the authors establish certain results concerning the Hadamard product for two classes related to starlike and convex univalent meromorphic functions of order @a and type @b with positive coefficients.

Differential subordination and superordination for certain subclasses of p-valent functions

In this paper we derive some subordination and superordination results for certain p-valent analytic functions in the open unit disc, which are acted upon by a class of extended multiplier transformations. Relevant connection of the results, which are presented in this paper with various known results are also considered.

Differential sandwich theorems for higher-order derivatives of p-valent functions defined by a linear operator

Abstract In this paper, we obtain some applications of first order differential subordination and superordination results for higher-order derivatives of p-valent functions involving a linear operator. Some of our results generalize previously known results.

The quasi-Hadamard product of certain analytic functions

Abstract The author establishes a theorem concerning the quasi-Hadamard product of certain analytic functions. The theorem and its applications improve the results due to Shigeyoshi Owa [S. Owa, On the subclasses of univalent functions, Math. Japon. 28 (1) (1983) 97–108].

Subordination and superordination properties of p -valent functions defined by a generalized fractional differintegral operator

Abstract For a generalized fractional differintegral operator associated with p- valent functions, we study different properties of differential subordination and superordination related to this operator.

On differential Sandwich theorems of analytic functions defined by generalized Sălăgean integral operator

In this paper we obtain some applications of first order differential subordination and superordination results involving generalized Sălăgean integral operator for certain normalized analytic functions. Some of our results generalize previously known results.

Some properties of certain classes of meromorphically p-valent functions involving extended multiplier transformations

In this paper, the authors investigate interesting properties of certain subclasses of meromorphically multivalent functions which are defined here by means of extended multiplier transformations.