Multivalent Analytic Functions Research Articles

Subordination properties of certain classes of multivalently analytic functions

By using a method based upon the principle of the Briot–Bouquet differential subordination, we obtain a sharp result for p -valently starlikeness of certain normalized and multivalently analytic functions. Our investigation of such families of multivalently analytic functions is motivated essentially by a recent study by Nunokawa et al. [M. Nunokawa, S. Owa, T. Sekine, R. Yamakawa, H. Saitoh and J. Nishiwaki, On certain multivalent functions, Internat. J. Math. Math. Sci. 2007 (2007) 1–5. Article ID 72393]. We also give an answer to the open problem which was posed in the aforementioned article by Nunokawa et al.

Subordination and superordination for multivalent functions associated with a class of fractional differintegral operators

The purpose of the present paper is to investigate some subordination and superordination implications associated with a class of fractional differintegral operators, which are obtained by considering suitable classes of admissible multivalent analytic functions. The sandwich-type theorems for these operators are also considered.

Majorization for certain classes of analytic functions using multiplier transformation

In the present paper we investigate the majorization properties for certain classes of multivalent analytic functions defined by multiplier transformation. Moreover, we point out some new or known consequences of our main result.

Certain subclasses of multivalent analytic functions defined by multiplier transforms

By making use of the principle of subordination between analytic functions and a family of multiplier transforms, we introduce and investigate some new subclasses of multivalent analytic functions. Such results as inclusion relationships, subordination and superordination properties, integral-preserving properties, argument estimates and convolution properties are proved.

Some subclasses of multivalent functions involving the extended fractional differintegral operator

The object of the present paper, is to investigate various properties of several sub- classes of multivalent analytic functions which are defined here by using the extended fractional differintegral operator Ω (λ,p) z (−∞ < λ < p+1; p ∈ N).

ON CERTAIN CLASSES OF MULTIVALENT FUNCTIONS INVOLVING A GENERALIZED DIFFERENTIAL OPERATOR

Making use of a generalized difierential operator we intro- duce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral pre- serving properties of these subclasses are also discussed.

Subordinations for multivalent analytic functions associated with the Dziok–Srivastava operator

Let 𝒜 p (p∈ℕ:={1, 2, 3, …}) be the class of functions f given by which are analytic in the open unit disk 𝕌. Making use of the method of differential subordinations, we obtain some sufficient conditions for f(z)∈𝒜 p involving the Dziok–Srivastava operator to satisfy certain subordination properties. The results presented here are shown not only to generalize the main results in several earlier investigations, but also to give rise to many other new results.

Certain subclasses of multivalent analytic functions involving the generalized Srivastava–Attiya operator

By making use of the principle of subordination between analytic functions and the generalized Srivastava–Attiya operator, we introduce and investigate some new subclasses of multivalent analytic functions. Such results as inclusion relationships and integral-preserving properties involving these subclasses are proved. Several subordination and superordination results associated with this operator are also derived.

A class of multivalently analytic functions associated with the Dziok–Srivastava operator

Making use of the familiar Dziok–Srivastava operator defined by means of a Hadamard product (or convolution), we introduce here a new class of multivalently analytic functions and investigate several interesting properties of this multivalently analytic function class. We also show how the results presented here are related to those in earlier works on the subject.

Inclusion and neighborhood properties for certain classes of multivalently analytic functions of complex order associated with the convolution structure

Making use of the familiar convolution structure of analytic functions, in this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order. Among the various results obtained here for each of these function classes, we derive the coefficient inequalities and other interesting properties and characteristics for functions belonging to the class introduced here.

Neighborhoods of a Certain Family of Multivalent Functions Defined by Using a Fractional Derivative Operator

Making use of a fractional derivative operator, we introduce and investigate two new classes $K_{j}(p,\lambda ,b,\beta )$ and $L_{j}(p,\lambda ,b,\beta ,\mu )$ of multivalently analytic functions of complex order. In this paper we obtain the coefficient estimates and inclusion relationships involving the $(j,\delta )-$ neighborhood of various subclasses of multivalently analytic functions of complex order.

Certain Results on Differential Subordination for Some Classes of Multivalently Analytic Functions Associated with a Convolution Structure

Appealing to the familiar convolution structure of analytic functions, we introduce a general class of multivalently analytic functions, and derive several properties and characteristics of this function class by applying the differential subordination techniques. Relevant connections of the results stated here with those obtained in earlier works are also pointed out.

Some properties of certain multivalent analytic functions involving the Cho–Kwon–Srivastava operator

By making use of the principle of subordination between analytic functions and the Cho–Kwon–Srivastava operator, we introduce a certain subclass of multivalent analytic functions. Such results as subordination and superordination properties, convolution properties, inclusion relationships, distortion theorems, inequality properties and sufficient conditions for multivalent starlikeness are proved. The results presented here would provide extensions of those given in earlier works. Several other new results are also obtained.

Subordinations for certain multivalent analytic functions associated with the generalized Srivastava–Attiya operator

In this paper, we investigate a new class of multivalent analytic functions defined by the generalized Srivastava–Attiya operator s, b . Several properties of functions belonging to this class are derived.

ON DIFFERENTIAL SUBORDINATIONS CONNECTED WITH BAZILOEVIC FUNCTIONS RELATED TO A SECTOR.

In this investigation we generalized the class introduced by J. patel [7] of multivalent analytic functions to the subclass which has been recently published. Also we derive various properties by using the techniques of Briat-Bouquet differential subordination.

Properties of certain subclasses of multivalent analytic functions involving the Dziok–Srivastava operator

In this paper, the authors introduce and investigate the various properties of two subclasses S p , k l , m ( α 1 ; h ) and K p , k l , m ( α 1 ; h ) of multivalent analytic functions. In particular, some sufficient conditions for the subclass S p , k l , m α 1 ; 1 + z 1 - z of analytic functions, argument properties, the growth theorems, distortion theorems and covering theorems are obtained. Some of the results, presented in this paper, would generalize and extend the corresponding results of earlier authors.

On a class of analytic multivalent functions

We use a property of the Bernardi operator in the theory of the Briot–Bouquet differential subordinations to prove several theorems for the classes V k p ( H ; A , B ) of multivalent analytic functions defined by using the Dziok–Srivastava operator H . Some of these results we obtain applying the convolution property due to Rusheweyh. We take advantage of the Miller–Mocanu lemma to improve the earlier result.

Some subclasses of multivalent analytic functions involving the Dziok–Srivastava operator

In the present paper, we introduce and investigate some new subclasses of multivalent analytic functions involving the Dziok–Srivastava operator. Such results as inclusion relationships, integral representations, convolution properties and integral-preserving properties for these function classes are proved. The results presented here would provide extensions of those given in earlier works. Several other new results are also obtained.

Some New Inclusion and Neighborhood Properties for Certain Multivalent Function Classes Associated with the Convolution Structure

We use the familiar convolution structure of analytic functions to introduce two new subclasses of multivalently analytic functions of complex order, and prove several inclusion relationships associated with the -neighborhoods for these subclasses. Some interesting consequences of these results are also pointed out.

Classes of multivalent analytic functions involving the Dziok–Srivastava operator

The object of the present paper is to investigate some inclusion relationships and a number of other useful properties of several subclasses of multivalent analytic functions, which are defined here by using the Dziok–Srivastava operator. Relevant connections of the results presented here with those obtained in earlier works are pointed out.