on meromorphically multivalent functions defined by multiplier transformation

On meromorphically multivalent functions defined by multiplier transformation

The purpose of this paper is to derive various useful subordination properties and characteristics for certain subclass of multivalent meromorphic functions, which are defined here by the multiplier transformation. Also, we obtained inclusion relationship for this subclass.

Subclasses of meromorphically multivalent functions defined by a differential operator

In this paper authors introduced two new subclasses ∑ρτςξ mp α, β, η and ∑ (α, β, η) + ρτςξ mp of meromorphically multivalent functions which aredefined by means of a new differential operator. By making use of the principle of differential subordination, authors investigate several inclusion relationships and properties of certain subclasses which are defined here by means of a differential op...

On Some Analytic Functions Defined by a Multiplier Transformation

Differential Subordinations for Certain Meromorphically Multivalent Functions Defined by Dziok-Srivastava Operator

and Applied Analysis 3 Corresponding to a function hp α1, . . . , αq; β1, . . . , βs; z defined by hp ( α1, . . . , αq; β1, . . . , βs; z ) z−pqFs ( α1, . . . , αq; β1, . . . , βs; z ) , 1.11 we now consider a linear operator Hp ( α1, . . . , αq; β1, . . . , βs ) : Σ ( p ) −→ Σp, 1.12 defined by means of the Hadamard product or convolution as follows: Hp ( α1, . . . , αq; β1, . . . , βs ) f z :...

Some properties of meromorphically multivalent functions

* 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.

A Class of Univalent Harmonic Functions Defined by Multiplier Transformation

A continuous function f(x+ iy) = u(x, y) + iv(x, y) defined in a domain D ⊂ C (Complex plane) is harmonic in D if u and v are real harmonic in D. Clunie and Shiel-Small [3] showed that in a simply connected domain such functions can be written in the form f = h+g, where both h and g are analytic. We call h the analytic part and g, the co-analytic part of f . Let w(z) = g ′(z) h′(z) be the dilat...