Harmonic Univalent Research Articles

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.

Investigating utilizations of harmonic univalent functions employing the Prabhakar fractional operator within specific categories

Investigating utilizations of harmonic univalent functions employing the Prabhakar fractional operator within specific categories

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.

Linear combination of convolution of harmonic univalent functions

Linear combination of convolution of harmonic univalent functions

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.

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

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.

Convolution and Coefficient Estimates for (p,q)-Convex Harmonic Functions Associated with Subordination

We preface and examine classes of (p, q)-convex harmonic locally univalent functions associated with subordination. We acquired a coefficient characterization of (p, q)-convex harmonic univalent functions. We give necessary and sufficient convolution terms for the functions we will introduce.

Unconstrained Optimization of Univalent Harmonic Functions

The new generalized operator , is a conjunction between Unconstrained optimization and Univalent Harmonic Functions.We derived some properties by this conjunction like, coefficient inequality, convex set, apply Bernardi operator and determine the extreme points such that In particular, the extreme points of  (  are { } and { }.

Harmonic spirallike functions and harmonic strongly starlike functions

In this note, we define two subclasses of normalized harmonic univalent functions of the unit disk, spirallike functions and strongly starlike functions, which preserve a hereditary property and have nice analytic and geometric characterizations. We also investigate the uniform boundedness and quasiconformal extendability of strongly starlike functions. Some coefficient conditions can be given for strong starlikeness and spirallikeness. We consider a special form of harmonic functions as an application.

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.

Moduli of Doubly Connected Domains Under Univalent Harmonic Maps

Moduli of Doubly Connected Domains Under Univalent Harmonic Maps

On Harmonic Univalent Functions Involving q-Poisson Distribution Series

On Harmonic Univalent Functions Involving q-Poisson Distribution Series

On Harmonic Functions by using Ruscheweyh-Type Associated with Differential Operators

By applying Ruscheweyh - type harmonic function on the class ASH(λ,α,k,γ), a new subclass ℋRq(m, α, k, γ) for harmonic univalent function in the unit disk D is introduced, Furthermore, some geometric properties are obtained such as distortion theorem, sufficient coefficient bounds ,extreme points and convex combination conditions for aforementioned subclass.