Harmonic Univalent Research Articles

On a new subclass of harmonic univalent functions defined by multiplier transformation

The purpose of the present paper is to introduce a new subclass of harmonic univalent functions by using Multiplier transformation. Coefficient estimates, distortion bounds, extreme points, convolution condition and convex combination for functions belonging to this class are determined. The results obtained for the class reduce to the corresponding several known results are briefly indicated.

Neighbourhoods of two new classes of harmonic univalent functions with varying arguments

Abstract In this paper, two new classes of harmonic univalent functions with varying arguments are defined by using planar harmonic convolution operator involving hypergeometric functions. Those classes are of special interest because they contain various classes of well-known harmonic univalent functions such as the classes of k-starlike and k-uniformly convex harmonic univalent functions. The main purpose of this paper is to investigate neighbourhoods of the classes in question.

Subclass of Harmonic Univalent Functions Defined by Modified Catas Operator

Subclass of Harmonic Univalent Functions Defined by Modified Catas Operator

A generalized class of Harmonic Univalent Functions associated with Salagean Operators Involving Convolutions

In this paper, we introduce a generalized class Si H (m,n, φ, ψ;α) , i ∈ {0, 1} of harmonic univalent functions. A sufficient coefficient condition for the normalized harmonic function to be in this class is obtained. It is also shown that this coefficient condition is necessary for its subclass T SH (m,n, φ, ψ;α). We further, obtain extreme points, bounds and a covering result for the class T SH (m,n, φ, ψ;α) and show that this class is closed under convolutions and convex combinations. In proving our results certain conditions on the coefficients of φ and ψ are considered which lead various well-known results proved earlier. 2000 Mathematics Subject Classification: 30C45, 30C50.

Constants and Characterization for Certain Classes of Univalent Harmonic Mappings

In this paper, we obtain growth, covering, and area theorems for certain families of sense preserving univalent harmonic functions which are close-to-convex in the unit disk \({\mathbb{D}}\). We present integral representation for the class that we have considered for our study. Representation of minimal surface associated with this class is also given whenever the second complex dilatation is a square of an analytic function. Also, we determine a general sufficient condition for a sense preserving harmonic function to be univalent and close-to-convex in \({\mathbb{D}}\). Finally, we examine the disk of univalency and close-to-convexity of certain classes of harmonic functions.

HARMONIC STARLIKENESS AND CONVEXITY OF INTEGRAL OPERATORS GENERATED BY GENERALIZED BESSEL FUNCTIONS

The present paper establishes connections between various subclasses of harmonic univalent functions by applying certain integral operator involving the generalized Bessel functions of first kind. To be more precise, we investigate such connections with harmonic starlike and harmonic convex mappings in the plane.

On a certain class of harmonic univalent functions defined by fractional calculus

The purpose of the present paper is to study a new subclass of harmonic univalent functions by using fractional calculus operator. We obtain coefficient conditions, extreme points, distortion bounds and radius of convexity for this class. We also show that the class studied in this paper is closed under convolution and convex combination and discuss a class preserving integral operator. The results obtained for this class reduce to the corresponding results for several known classes in the literature are briefly indicated.

Coefficient conditions for harmonic univalent mappings and hypergeometric mappings

In this paper, we obtain coefficient criteria for a normalized harmonic function defined in the unit disk to be close-to-convex and fully starlike, respectively. Using these coefficient conditions, we present different classes of harmonic close-to-convex (resp. fully starlike) functions involving Gaussian hypergeometric functions. In addition, we present a convolution characterization for a class of univalent harmonic functions discussed recently by Mocanu, and later by Bshouty and Lyzzaik in 2010. Our approach provide examples of harmonic polynomials that are close-to-convex and starlike, respectively.

Some connections between various subclasses of planar harmonic mappings involving generalized Bessel functions

The purpose of the present paper is to establish connections between various subclasses of harmonic univalent functions by applying certain convolution operator involving generalized Bessel functions of first kind. To be more precise, we investigate such connections with harmonic \(k\)-uniformly convex and harmonic \(k\)-uniformly starlike mappings in the plane.

Convolution properties of the harmonic Koebe function and its connection with 2-starlike mappings

In 1984, Clunie and Sheil-Small constructed the harmonic Koebe function expecting it to play the role of extremal function for extremal problems over the class of sense-preserving harmonic univalent functions suitably normalized in the open unit disc. In this paper, we investigate the convolution properties of . In addition, we discuss the geometric properties of -starlike functions defined using the Sălăgean differential operator. Given a -starlike function , the product is shown to be univalent and convex in the direction of the real axis.

Several properties of certain classes of univalent harmonic functions

In this paper we investigate several properties of two classes of harmonic univalent functions. Some of our results improve previously known results.

Partial sums of a certain harmonic univalent meromorphic functions

In the present paper we determine sharp lower bounds of the real part of the ratios of harmonic univalent meromorphic functions to their sequences of partial sums. Let H denote the class of functions f that are harmonic univalent and sense-preserving in U =;fz :jzj > 1g which are of the form

Analytic and Harmonic Univalent Functions

Analytic and Harmonic Univalent Functions

Construction of harmonic univalent mappings convex in one direction

In the present paper, we derive several conditions of linear combinations and convolutions of harmonic mappings to be univalent and convex in one direction, one of them gives a partial answer to an open problem proposed by Dorff. The results presented here provide extensions and improvements of those given in some earlier works. Several examples of univalent harmonic mappings convex in one direction are also constructed to demonstrate the main results.

On Certain Subclass of Harmonic Starlike Functions

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

On Harmonic Functions Defined by Differential Operator with Respect tok-Symmetric Points

We introduce new classesMHkσ,s(λ,δ,α)andM¯Hkσ,s(λ,δ,α)of harmonic univalent functions with respect tok-symmetric points defined by differential operator. We determine a sufficient coefficient condition, representation theorem, and distortion theorem.

Some Properties of Certain Classes of Harmonic Univalent Functions

Some Properties of Certain Classes of Harmonic Univalent Functions

A Subclass of Harmonic Univalent Functions Associated with -Analogue of Dziok-Srivastava Operator

We study a class of complex-valued harmonic univalent functions using a generalized operator involving basic hypergeometric function. Precisely, we give a necessary and sufficient coefficient condition for functions in this class. Distortion bounds, extreme points, and neighborhood of such functions are also considered.

A Brief Study of Certain Class of Harmonic Functions of Bazilevič Type

We define and investigate a new subclass of Bazilevič type harmonic univalent functions using a linear operator. We investigated the harmonic structures in terms of its coefficient conditions, extreme points, distortion bounds, convolution, and convex combination. So, also, we discussed the subordination properties for the functions in this class.

On close-to-convex harmonic mappings

We continue to investigate the relation of close-to-convex harmonic mappings versus their analytic counterpart. Our starting point is the investigation initiated by Clunie and Sheil-Small [J. Clunie and T. Sheil-Small, Harmonic univalent mappings, Ann. Acad. Sci. Fenn. Ser. A.I. Math. 9 (1984), pp. 3–25] and further developments by Chuaqui and Hernandez [M. Chuaqui and R. Hernandez, Univalent harmonic mappings and linearly connected domains, J. Math. Anal. Appl. 332 (2007), pp. 1189–1194], and Bshouty and Lyzzaik [D. Bshouty and A. Lyzzaik, Close-to-convexity criteria for planar harmonic mappings, Complex Anal. Oper.Theory (to appear)].