Class Of Harmonic Univalent Functions Research Articles

On Harmonic Univalent Functions Defined by Dziok-Srivastava Operator

The purpose of this work is to present a class of harmonic univalent functions defined by the Dziok-Srivastava operator. Some geometric properties like coefficients conditions, distortion theorem, convolution (Hadamard product), convex combination and extreme points are investigated.
 2000 Mathematics Subject Classification: 30C45, 30C50

Improved Bohr inequalities for certain class of harmonic univalent functions

Let be the class of complex-valued harmonic mappings defined in the unit disk , where h and g are analytic functions in with the normalization and . Let Let be the class of harmonic univalent mappings in the unit disk [Ghosh N, Allu V. On some subclasses of harmonic mappings. Bull Aust Math Soc. 2020;101:130–140.]. In this paper, we obtain the sharp Bohr–Rogosinski inequality, improved Bohr inequality, refined Bohr inequality and Bohr-type inequality for the class .

A New Class of Harmonic Univalent Functions of the Salagean Type

A new family of Salagean type harmonic univalent functions is described and investigated. For the functions in this class, we derive coefficient inequalities, extreme points, and distortion limits.

A Class of k-Symmetric Harmonic Functions Involving a Certain q-Derivative Operator

In this paper, we introduce a new class of harmonic univalent functions with respect to k-symmetric points by using a newly-defined q-analog of the derivative operator for complex harmonic functions. For this harmonic univalent function class, we derive a sufficient condition, a representation theorem, and a distortion theorem. We also apply a generalized q-Bernardi–Libera–Livingston integral operator to examine the closure properties and coefficient bounds. Furthermore, we highlight some known consequences of our main results. In the concluding part of the article, we have finally reiterated the well-demonstrated fact that the results presented in this article can easily be rewritten as the so-called (p,q)-variations by making some straightforward simplifications, and it will be an inconsequential exercise, simply because the additional parameter p is obviously unnecessary.

A Class of Harmonic Univalent Functions Defined by Differential Operator and the Generalization

In this paper, a new class of harmonic univalent functions was defined by the differential operator. We obtained some geometric properties, such as the coefficient estimates, convex combination, extreme points, and convolution (Hadamard product), which are required

A class of harmonic functions associated with a generalized differential operator

We introduce a new class of harmonic univalent functions by using a generalized differential operator and investigate some of its geometric properties, like, coefficient estimates, extreme points and inclusion relations. Finally, we show that this class is invariant under Bernandi-Libera-Livingston integral for harmonic functions.

On the Generalization of a Class of Harmonic Univalent Functions Defined by Differential Operator

In this article, a new class of harmonic univalent functions, defined by the differential operator, is introduced. Some geometric properties, like, coefficient estimates, extreme points, convex combination and convolution (Hadamard product) are obtained.

Generalized Convolution of Certain Class of Harmonic Univalent Functions

Generalized Convolution of Certain Class of Harmonic Univalent Functions

A New Subclass of Harmonic Univalent Functions

In this paper, we define a new class of harmonic univalent functions of the form in the open unit disk . We obtain basic properties, like, coefficient bounds, extreme points, convex combination, distortion and growth theorems and integral operator.

Coefficient inequalities for a class of harmonic univalent functions

In this paper, a new class of harmonic univalent function using the modified Salagean differential operator is introduced. New results on the new class are obtained. Distortion bounds, Convolution and Convex combination in the new class are also established. The work extended some earlier results .

Convolution on a Generalized Class of Harmonic Univalent Functions

In the present paper, we introduce new subclasses of harmonic univalent functions and establish certain results concerning the convolution of functions for these subclasses. Relevant connections of the results presented here with various known results are briefly indicated.

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.

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.

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.

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

The purpose of the present paper is to study a certain subclass of harmonic univalent functions associated with Dziok-Srivastava operator. We obtain coefficient conditions, distortion bounds, and extreme points for the above class of harmonic univalent functions belonging to this class and discuss a class preserving integral operator. We also show that class studied in this paper is closed under convolution and convex combination. The results obtained for the class reduced to the corresponding results for several known classes in the literature are briefly indicated.

Subclass of Harmonic Univalent Functions Associated with Generalized Derivative Operator

Using a generalized derivative operator, we introduce and study a new subclass of harmonic univalent functions. In the present paper, we obtain numerous sharp results including coefficient conditions, extreme points, convolution properties and convex combinations for the above class of harmonic univalent functions. The results obtained for the class reduce to the corresponding results for various well-known classes in the literature.

A new class of harmonic univalent functions by the generalized Salagean operator

A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form \(f = h + \bar g\), where h and g are analytic in U. We define and investigate a new class SHPλ(α, β) by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ(α,β). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.

A new class of Salagean-type harmonic univalent functions

We define and investigate a new class of Salagean-type harmonic univalent functions. We obtain coefficient conditions, extreme points, distortion bounds, convex combination and radii of convex for the above class of harmonic univalent functions.