Multiplier Transformations Research Articles

Some properties of certain meromorphically multivalent functions associated with the extended multiplier transformation

The main object of the present paper is to investigate some interesting properties of certain meromorphically multivalent functions associated with the extended multiplier transformation.

A note on certain meromorphic [formula omitted]-valent functions

In this work the author introduces a certain multiplier transformation for meromorphic p -valent functions which are analytic in U ∗ . The object of this work is to give an application of this operator to the differential inequalities.

On Sufficient Conditions for Certain Subclass of Analytic Functions Defined by Convolution

In the present investigation sufficient conditions are found for certain subclass of normalized analytic functions defined by Hadamard product. Differential sandwich theorems are also obtained. As a special case of this we obtain results involving Ruscheweyh derivative, Slgean derivative, Carlson-shaffer operator, Dziok-Srivatsava linear operator, Multiplier transformation.

Differential subordination and superordination of analytic functions defined by the multiplier transformation

Differential subordination and superordination results are obtained for analytic functions in the open unit disk which are associated with the multiplier transformation. These results are obtained by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained. Mathematics subject classification (2000): 30C80, 30C45.

Inclusion properties of certain subclass of analytic functions defined by multiplier transformations

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Neighborhoods of a certain class of analytic functions with negative coefficients

A certain subclass of analytic functions in the open unit disc with negative coefficients is introduced. The new class is defined by means of multiplier transformations. By making use of the familiar concept of neighborhoods of analytic function, the author proves coefficient inequalities, distortion theorems and associated inclusion relations for the $(n,\delta)$-neighborhoods of functions belonging to the new class, which satisfy a certain nonhomogeneous Cauchy-Euler differential equation.

On differential sandwich theorems for some subclasses of analytic functions associated with multiplier transformation

The purpose of this present article is to derive some subordination and superordination results for certain normalized analytic functions in the open unit disk, acted upon by a class of multiplier transformations.

The Radius of Starlikeness of the Certain Classes of -Valent Functions Defined by Multiplier Transformations

The aim of this paper is to give the radius of starlikeness of the certain classes of -valent functions defined by multiplier transformations. The results are obtained by using techniques of Robertson (1953,1963) which was used by Bernardi (1970), Libera (1971), Livingstone (1966), and Goel (1972).

Differential Subordinations Associated with Multiplier Transformations

The authors introduce new classes of analytic functions in the open unit disc which are defined by using multiplier transformations. The properties of these classes will be studied by using techniques involving the Briot-Bouquet differential subordinations. Also an integral transform is established.

Convolutions and multiplier transformations of convex bodies

Rotation intertwining maps from the set of convex bodies in into itself that are continuous linear operators with respect to Minkowski and Blaschke addition are investigated. The main focus is on Blaschke-Minkowski homomorphisms. We show that such maps are represented by a spherical convolution operator. An application of this representation is a complete classification of all even Blaschke-Minkowski homomorphisms which shows that these maps behave in many respects similar to the well known projection body operator. Among further applications is the following result: If an even Blaschke-Minkowski homomorphism maps a convex body to a polytope, then it is a constant multiple of the projection body operator

Subclasses of meromorphic functions associated with the Cho–Kwon–Srivastava operator

We consider a multiplier transformation and some subclasses of the class of meromorphic functions which was defined by means of the Hadamard product by N.E. Cho, O.S. Kwon and H.M. Srivastava in [N.E. Cho, O.S. Kwon, H.M. Srivastava, Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations, J. Math. Anal. Appl. 300 (2004) 505–520].

On Some Analytic Functions Defined by a Multiplier Transformation

We introduce and study a new class of analytic functions defined in the unit disc using a certain multiplier transformation. Some inclusion results and other interesting properties of this class are investigated.

Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformations

The purpose of this article is to derive some subordination and superordination results for certain families of normalized analytic functions in the open unit disk, which are acted upon by a class of multiplier transformations. Relevant connections of the results, which are presented in this article, with various known results are also considered.

Inclusion properties of certain subclasses of analytic functions defined by a multiplier transformation

Let A denote the class of analytic functions with the normalization ƒ (0) = ƒ′(0)-1 = 0 in the open unit disk U, set f λ s ( z ) = z + ∑ k = 2 ∞ ( k + λ 1 + λ ) s z k ( s ∈ ℝ ; λ > - 1 ; z ∈ U ) and define ƒ λ,μ s , in terms of the Hadamard product f λ s ( z ) ∗ f λ , μ s ( z ) = z ( 1 − z ) μ ( μ > 0 ; z ∈ U ) In this paper, the authors introduce several new subclasses of analytic functions defined by means of the operator I λ,μ s : A → A, given by I λ , μ s f ( z ) = f λ , μ s ( z ) ∗ f ( z ) ( f ∈ A ; s ∈ ℝ ; λ > - 1 ; μ > 0 ) Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

Inclusion relationships for certain subclasses of meromorphic functions associated with a family of multiplier transformations

The purpose of the present article is to introduce several new subclasses of meromorphic functions defined by using the multiplier transformation and investigate various inclusion relationships for these subclasses. Some interesting applications involving a certain class of integral operators are also considered.

Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations

Making use of a multiplier transformation, which is defined here by means of the Hadamard product (or convolution), the authors introduce some new subclasses of meromorphic functions and investigate their inclusion relationships and argument properties. Some integral-preserving properties in a given sector are also considered.

Inequalities Involving Certain Families of Integral and Convolution Operators

The main object of the present paper is to derive several strict inequalities associated with some families of integral and convolution operators which are defined for the class of normalized analytic functions in the open unit disk. A number of interesting consequences of these inequalities are also considered. Mathematics subject classification (2000): 30C45, 26A33, 33B15. Keywordsandphrases: Integral operators, convolutionoperators, analytic functions, Hadamardproduct or convolution, multiplier transformation, fractional integral, fractional derivative, Ruscheweyh derivative, Jack’s lemma.

Superintegrable systems in Darboux spaces

Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of revolution that have at least two integrals of motion quadratic in the momenta, in addition to the Hamiltonian. These are two-dimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2-space or on the complex 2-sphere, via “coupling constant metamorphosis” (or equivalently, via Stäckel multiplier transformations). We present a table of the results.

MULTIPLIER TRANSFORMATIONS AND STRONGLY CLOSE-TO-CONVEX FUNCTIONS

The purpose of the present paper is to introduce some new subclasses of strongly close-to-convex functions in the open unit disk defined by multiplier transformations and study their properties. Our results include several previous known results as special cases.

Argument estimates of certain analytic functions defined by a class of multiplier transformations

The purpose of the present paper is to derive some inclusion properties and argument estimates of certain normalized analytic functions in the open unit disk, which are defined by means of a class of multiplier transformations. Furthermore, the integral preserving properties in a sector are investigated for these multiplier transformations. Relevant connections of the results, which are presented in this paper, with various known results are also considered.