Properties Of Certain Subclasses Research Articles

Inclusion Properties for Certain Subclasses of Analytic Functions Defined by a Linear Operator

The purpose of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions associated with a family of linear operators, which are defined by means of the Hadamard product (or convolution). Some integral preserving properties are also considered.

Some inclusion properties for certain subclasses of strongly starlike and strongly convex functions involving a family of fractional integral operators

A known family of fractional integral operators (with the Gauss hypergeometric function in the kernel) is used here to define some new subclasses of strongly starlike and strongly convex functions of order β and type α in the open unit disk 𝕌. For each of these new function classes, several inclusion relationships associated with the fractional integral operators are established. Some interesting corollaries and consequences of the main inclusion relationships are also considered.

Convolution properties for certain classes of multivalent functions

Recently N.E. Cho, O.S. Kwon and H.M. Srivastava [Nak Eun Cho, Oh Sang Kwon, H.M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl. 292 (2004) 470–483] have introduced the class S a , c λ ( η ; p ; h ) of multivalent analytic functions and have given a number of results. This class has been defined by means of a special linear operator associated with the Gaussian hypergeometric function. In this paper we have extended some of the previous results and have given other properties of this class. We have made use of differential subordinations and properties of convolution in geometric function theory.

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].

Some inclusion relationships and integral-preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators

The object of the present paper is to investigate a family of integral operators defined on the space of normalized meromorphic functions. By making use of these novel integral operators, we introduce and investigate several new subclasses of starlike, convex, close-to-convex, and quasi-convex meromorphic functions. In particular, we establish some inclusion relationships associated with the aforementioned integral operators. Several interesting integral-preserving properties are also considered.

Inclusion Properties for Certain Subclasses of Analytic Functions Associated with the Dziok-Srivastava Operator

The purpose of the present paper is to introduce several new classes of analytic functions defined by using the Choi-Saigo-Srivastava operator associated with the Dziok-Srivastava operator and to investigate various inclusion properties of these classes. Some interesting applications involving classes of integral operators 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.

Some classes of analytic functions involving Noor integral operator

The object of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions defined by using the Noor integral operator. The integral preserving properties in connection with the operator are also considered. Relevant connections of the results presented here with those obtained in earlier works are pointed out.

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.

Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators

By making use of a general linear operator I p λ(a,c) , the authors introduce several new subclasses of multivalent functions and investigate various inclusion relationships and argument properties associated with these subclasses. Some interesting applications involving such and other families of linear operators are also considered. The results presented here include a number of known results as their special cases.

CERTAIN CLASSES OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS

Let $\Sigma_p$ denote the class of functions of the form \[f(z)=\frac{a_{-1}}{z}+\sum_{k=1}^\infty a_kz^k \quad (a_k\ge 0, a_{-1}>0)\] which are analytic in the annulus $D =\{z |0< |z|<1\}$. Let $\Sigma_{p,1}$ and $\Sigma_{p,2}$ denote subclasses of $\Sigma_p$ satisfying $f(z_0)=1/z_0$ and $f'(z_0)=-1/z^2_0$ ($-1<z_0<1$, $z_0\neq 0$), respectively. Properties of certain subclasses of $\Sigma_{p,1}$ and $\Sigma_{p,2}$ are investigated and sharp results are obtained. Also a new characterization for certain subclass of $\Sigma_p$ is proved.