Punctured Unit Disk Research Articles

SUFFICIENT CONDITIONS FOR MEROMORPHIC CLOSE-TO-CONVEX FUNCTIONS

The object of the present paper is to consider some sufficient conditions for meromorphic close-to-convex functions in the punctured unit disc.

Certain Subclasses Of Meromorphically Multivalent Functions Involving New Linear Operator

The main object of this article is to study the subclasses of multivalent meromorphic functions by using a linear operator in punctured unit disk. Some geometric properties like coefficients bound, distortion theorems and convolutions property are investigated.

Certain Sufficient Conditions for Starlikeness and Convexity of Meromorphically Multivalent Functions

In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.

On Certain Subclass of Meromorphic Close-to-Convex Functions

Abstract In this paper we introduce and investigate a certain subclass of functions which are analytic in the punctured unit disk and meromorphically close-to-convex. The sub-ordination property, inclusion relationship, coefficient inequalities, distortion theorem and a sufficient condition for our subclass of functions are derived. The results presented here would provide extensions of those given in earlier works.

Sufficient Conditions for Meromorphically p-Valent Starlikeness and Close-to-Convexity

Making use of the linear operator Iλm defined by (Frasin 2012), we introduce the class 𝕄p,jm(λ,μ,α) of meromorphically p-valent functions in the punctured unit disk 𝒰∗. Furthermore, we obtain some sufficient conditions for starlikeness and close-to-convexity for functions belonging to this class. Several corollaries and consequences of the main results are also considered.

A Study of a Certain Subclass of Hurwitz-Lerch-Zeta Function Related to a Linear Operator

By using a linear operator with Hurwitz-Lerch-Zeta function, which is defined here by means of the Hadamard product (or convolution), the author investigates interesting properties of certain subclasses of meromorphically univalent functions in the punctured unit disk .

Subordination and inclusion theorems for subclasses of meromorphic functions with applications to electromagnetic cloaking

In this paper subordination and inclusion relations are studied for some subclasses of multivalent meromorphic functions in the punctured unit disc having a pole of order p at the origin. The subclasses under investigation are defined through combinations and iterations of a meromorphic analogue of the Cho–Kwon–Srivastava operator for normalized analytic functions. Specially, emphasis is given in this study on the effect of the increase of different parameters on the size of the subclasses. Applications are indicated for the subordination results to electromagnetic cloaking.

Differential operator of meromorphic p-valent functions

A certain differential operator $ I_{λ}^{m}f(z) $ is introduced for functions of the form $f(z)=(1/(z^{p}))+∑_{n=k}^{∞}a_{n+p-1}z^{n+p-1} $ which are $p$-valent in the punctured unit disk $U^{∗}=\{z:z∈C \text{ and } 0<|z|<1\},$ where $p$ and $ k $ are positive integers. The main object of this paper is to give an application of the operator $I_{λ}^{m}f(z)$ to the differential inequalities.

Differential operator of meromorphic p-valent functions

A certain differential operator $ I_{λ}^{m}f(z) $ is introduced for functions of the form $f(z)=(1/(z^{p}))+∑_{n=k}^{∞}a_{n+p-1}z^{n+p-1} $ which are $p$-valent in the punctured unit disk $U^{∗}=\{z:z∈C \text{ and } 0<|z|<1\},$ where $p$ and $ k $ are positive integers. The main object of this paper is to give an application of the operator $I_{λ}^{m}f(z)$ to the differential inequalities.

On certain class of meromorphic functions with positive coefficients

In the present investigation we define a new class of meromorphic functions on the punctured unit disk Δ*:={z∈ℂ:0<|z|<1} by making use of the generalized Dziok–Srivastava operator Hml[α1]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.

Inclusion Relationships for Certain Subclasses of Meromorphic Functions Defined by Using the Extended Multiplier Transformations

Let denote the class of analytic functions in the punctured unit disc . Set , and define in terms of the Hadamard product by . In this paper, we introduce several new subclasses of analytic functions defined by means of the operator Inclusion properties of these classes and some applications involving integral operator are also considered.

On inclusion relationships of certain subclasses of meromorphic functions involving integral operator

In this paper, we introduce some subclasses of meromorphic functions in the punctured unit disc. Several inclusion relationships and some other interesting properties of these classes are discussed.

On Certain Classes of Meromorphic Functions Associated with Conic Domains

Making use of the concept of k‐uniformly bounded boundary rotation and Ruscheweyh differential operator, we introduce some new classes of meromorphic functions in the punctured unit disc. Convolution technique and principle of subordination are used to investigate these classes. Inclusion results, generalized Bernardi integral operator, and rate of growth of coefficients are studied. Some interesting consequences are also derived from the main results.

A Subclass of Meromorphic Close-to-Convex Functions of Janowski's Type

We introduce a subclass Σ(𝐴,𝐵)(−1≤𝐵<𝐴≤1) of functions which are analytic in the punctured unit disk and meromorphically close-to-convex. We obtain some coefficients bounds and some argument and convolution properties belonging to this class.

Certain studies of the Liu-Srivastava linear operator on meromorphic functions

Motivated by the Liu-Srivastava linear operator, we introduce here a modification of the operator of multivalent meromorphic functions in the punctured unit disk. A new subclass of analytic functions involving this operator is given. Some sufficient conditions for star-likeness, which generalize and refine some previous results were determined. Key words: Hypergeometric function, Liu-Srivastava linear operator, convolution, meromorphic function, univalent functions, starlike functions, convex functions, -convex function, Carlson-Shaffer linear operator, Ruscheweyh derivative operator.

Differential Sandwich Theorem for Multivalent Meromorphic Functions associated with the Liu-Srivastava Operator

Differential subordination and superordination results are obtained for multivalent meromorphic functions associated with the Liu-Srivastava linear operator in the punctured unit disk. These results are derived by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained.

Hyperbolic embeddability of locally complete almost complex submanifolds

In this Note, we generalize to the almost complex setting, a theorem of Zaidenberg (1983) [13] and Thai (1991) [12] by giving a characterization on hyperbolic embeddability of a locally complete and relatively compact almost complex submanifold in terms of extension of pseudo-holomorphic disks from the punctured unit disk and of limit J-complex lines.

Normal pseudoholomorphic curves

First, we give some characterizations of J-hyperbolic points for almost complex manifolds. We apply these characterizations to show that the hyperbolic embeddedness of an almost complex submanifold is given by a relative compactness of certain spaces of continuous extensions of pseudoholomorphic curves defined on the punctured unit disc. Next, we define uniformly normal families of pseudoholomorphic curves. We prove extension-convergence theorems for these families similar to those obtained by Kobayashi, Kiernan and Joseph-Kwack in the standard complex case.

Discontinuous solutions to the two-valued minimal surface equation

Recently, the author gave an asymptotic geometric description near the origin of any solution to the Two-Valued Minimal Surface Equation defined over the punctured unit disk 𝒟\{0} in , determined by whether the solution can be extended continuously across the origin. Here, we study discontinuous solutions, in particular giving conditions on the boundary data ensuring the solution is of this type.

Subordination and superordination of a certain integral operator on meromorphic functions

Using the methods of differential subordination and superordination, sufficient conditions on the integral operator of meromorphic functions in the punctured unit disk for obtaining, respectively, the best dominant and the best subordinant are determined. New Sandwich-type results are also obtained.