Subclass Of Harmonic Univalent Functions Research Articles

Subclass of Harmonic Univalent Functions Connected with Hypergeometric Functions

In this paper, we introduce and define a new subclass of harmonic univalent functions involving hypergeometric functions which are sense-preserving in the open unit disc. Further we obtain the coefficient bounds, extreme points, convex combination, growth bounds, distortion bounds and integral operator for this class.

A new subclass of harmonic univalent functions associated with q-calculus

The purpose of the present paper is to introduce a new subclass of harmonic univalent functions by applying q-calculus. Coefficient inequalities, extreme points, distortion bounds, covering results, convolution condition and convex combination are determined for this class. Finally, we discuss a class preserving integral operator for this class.

On Janowski Type Harmonic Functions Associated with the Wright Hypergeometric Functions

In our present study we consider Janowski type harmonic functions class introduced and studied by Dziok, whose members are given by $h(z) = z + \sum_{n=2}^{\infty} h_n z^n$ and $g(z) = \sum_{n=1}^{\infty} g_n z^n$, such that $\mathcal{ST}_{H}(F,G)=\big\{ f = h + \bar{g} \in {H}:\frac{\mathfrak{D}_H f(z)}{f(z)}\prec\frac{1+Fz}{1+G z};\, (-G \leq F < G \leq 1, \text{ with } g_1=0)\big\},$ where $\mathfrak{D}_H f(z) = zh'(z)-\overline{zg'(z)}\,$ and $z\in \mathbb{U}=\{z:z\in \mathbb{C} \text{ and }|z| < 1 \}.$ We investigate an~association between these subclasses of harmonic univalent functions by applying certain convolution operator concerning Wright's generalized hypergeometric functions and several special cases are given as a corollary. Moreover we pointed out certain connections between Janowski-type harmonic functions class involving the generalized Mittag–Leffler functions. Relevant connections of the results presented herewith various well-known results are briefly indicated.

On Bohr's inequality for special subclasses of stable starlike harmonic mappings

Abstract The focus of this article is to explore the Bohr inequality for a specific subset of harmonic starlike mappings introduced by Ghosh and Vasudevarao (Some basic properties of certain subclass of harmonic univalent functions, Complex Var. Elliptic Equ. 63 (2018), no. 12, 1687–1703.). This set is denoted as ℬ H 0 ( M ) ≔ { f = h + g ¯ ∈ ℋ 0 : ∣ z h ″ ( z ) ∣ ≤ M − ∣ z g ″ ( z ) ∣ } {{\mathcal{ {\mathcal B} }}}_{H}^{0}\left(M):= \{f=h+\overline{g}\in {{\mathcal{ {\mathcal H} }}}_{0}:| z{h}^{^{\prime\prime} }\left(z)| \le M-| z{g}^{^{\prime\prime} }\left(z)| \} for z ∈ D z\in {\mathbb{D}} , where 0 < M ≤ 1 0\lt M\le 1 . It is worth mentioning that the functions belonging to the class ℬ H 0 ( M ) {{\mathcal{ {\mathcal B} }}}_{H}^{0}\left(M) are recognized for their stability as starlike harmonic mappings. With this in mind, this research has a twofold goal: first, to determine the optimal Bohr radius for this specific subclass of harmonic mappings, and second, to extend the Bohr-Rogosinski phenomenon to the same subclass.

Application of Integral Operator Generated by Touchard Polynomials to Certain Subclasses of Harmonic Functions

Let SH denote the class of functions f = h + g which are harmonic univalent and sense-preserving in the unite disk U = {z : |z| < 1} where h(z) = z +P∞ k=2 akzk, g(z) =∞Pk=1 bkzk (|b1| < 1). In this paper we establish connections between various subclasses of harmonic univalent functions by applying certain integral operator involving the Touchard Polynomials.

Some Sub-Classes of Harmonic Univalent functions

Complex Analysis is branch of Geometric function theory. Geometric function theory concerned with interplay between the geometric properties of the image domain and analytic properties of the mapping functions. Some properties of analytic functions are exclusive and do not extend to more general harmonic mappings. In this paper we study the some subclasses of univalent harmonic functions like Coefficient Bounds, Distortion results and Convolution of Two functions.

$q$-analogue of a class of harmonic functions

The purpose of the present paper is to introduce a new subclass of harmonic univalent functions associated with a $q$-Ruscheweyh derivative operator. A necessary and sufficient convolution condition for the functions to be in this class is obtained. Using this necessary and sufficient coefficient condition, results based on the extreme points, convexity and compactness for this class are also obtained.

A Study of Spiral-Like Harmonic Functions Associated with Quantum Calculus

This article introduces new subclasses of harmonic univalent functions associated with q -difference operator. Modified q -multiplier transformation is defined, and certain geometric properties such as the sufficient condition, distortion result, extreme points, and invariance of convex combination of the elements of the subclasses are discussed by employing the newly defined q -operator. Also, various well-known results already proved in the literature are pointed out.

A New Subclass of Harmonic Univalent Functions Defined by a Linear Operator

In this paper, a new subclass of complex-valued harmonic univalent functions f(z)=h(z)+g(z)¯¯¯¯¯¯¯¯¯ in the open disk U={z:z∈C and |z|<1} defined by using a linear operator. We investigate coefficient condition, extreme points, distortion and convex combination for this subclass.

Certain subclass of harmonic univalent functions defined by q-differential operator

In this paper, we define certain subclass of harmonic univalent function in the unit disc \(U = \left\{ {z \in C:\left| z \right| < 1} \right\}\) by using \(q\)-differential operator. Also we obtain coefficient inequalities, growth and distortion theorems for this subclass.

Q-Analogue of New Subclass of Salagean-type Harmonic Univalent Functions defined by Subordination

We introduce and investigate q-analogue of a new subclass of Salagean-type harmonic univalent functions defined by subordination. We first obtained a coefficient characterization of these functions. We give necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for this subclass of harmonic univalent functions with negative coefficients.

Q-Analogue of a New Subclass of Harmonic Univalent Functions Associated with Subordination

In this article, we introduce and investigate the q-analogue of a new subclass of harmonic univalent functions defined by subordination. We first obtain a coefficient characterization of these functions. We give compactness and extreme points, distortion bounds, necessary and sufficient convolution conditions for this subclass of harmonic univalent functions with negative coefficients. The symmetry properties and other properties of the q-analogue subclass of functions presented in this paper shed light on future studies.

On New Subclass of Harmonic Univalent Functions Associated with Modified q-Operator

In this article, we introduce new subclasses of harmonic univalent functions associated with the q-difference operator. The modified q-Srivastava-Attiya operator is defined and certain applications of this operator are discussed. We investigate the sufficient condition, distortion result, extreme points and invariance of convex combination of the elements of the subclasses.

On Harmonic Univalent Functions Involving (p,q)-Poisson Distribution Series

Harmonic functions are a classic title in the class of geometric functions. Many researchers have studied these function classes from past to present, and since it has a wide range of applications, it is still a popular class. In this study, we will examine harmonic univalent functions, a subclass of harmonic functions. In this study, a subclass of harmonic univalent functions will be examined. Let H denote the class of continuous complex-valued harmonic functions which are harmonic in the open unit disk U={z ϵ C∶|z| |g'(z)| (see [3]). Throughout this paper, we will use introductory notations and delineations of the (p, q)- calculus. The aim of the present paper is to find connections between (p,q)-starlike harmonic univalent functions involving (p,q)-Poisson distribution series.

On Convolution and Convex Combination of Harmonic Mappings

In this paper, the subclass of harmonic univalent functions by shearing construction is studied and this subclass of harmonic mappings needs a necessary and adequate condition to be convex in the horizontal direction. Furthermore, convolutions of two special subclasses of univalent harmonic mappings are shown to be convex in the horizontal direction. Also, the family of univalent harmonic mappings of the unit disk onto a region convex in the direction of the imaginary axis is introduced. Sufficient conditions for convex combinations of harmonic mappings of this family to be univalently convex in the direction of the imaginary axis are obtained.

Certain subclass of harmonic univalent functions associated with generalized hypergeometric functions

In this paper, we introduce and define a new subclass of harmonic univalent functions involving generalized hypergeometric functions which are sense-preserving in the open unit disc. Further we obtain the coefficient bounds, extreme points, convex combination, growth bounds, distortion bounds and integral operator for this class.

SUBCLASS OF HARMONIC UNIVALENT FUNCTIONS DEFINED BY DIFFERENTIAL OPERATOR

In this paper, using Differential operator a certain subclass of harmonic univalent functions in the unit disc U = {z ∈ C : |z| < 1} is investigated. Some properties such as coefficient bounds, convex combination, extreme points and convolution conditions of this class are obtained. The newly introduced subclass of harmonic univalent functions is more general than the subclasses earlier found in the literature.

Mapping properties of Janowski-type harmonic functions involving Mittag-Leffler function

<abstract><p>In this paper, we examine a connotation between certain subclasses of harmonic univalent functions by applying certain convolution operator regarding Mittag-Leffler function. To be more precise, we confer such influences with Janowski-type harmonic univalent functions in the open unit disc $ \mathbb{D}. $</p></abstract>

An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function

The main purpose of this paper is to establish connections between various subclasses of harmonic univalent functions by applying certain convolution operator involving hypergeometric functions. We investigate such connections with Goodman- Salagean-Type harmonic univalent functions in the open unit disc U.

Inclusion Relation between Various Subclasses of Harmonic Univalent Functions Associated with Wright’s Generalized Hypergeometric Functions

The purpose of the present paper is to obtain some inclusion relation between various subclasses of harmonic univalent functions by applying certain convolution operators associated with Wright’s generalized hypergeometric functions.