Subclass Of Harmonic Functions Research Articles

Sharp Estimates Involving a Generalized Symmetric Sălăgean q-Differential Operator for Harmonic Functions via Quantum Calculus

In this study, we apply q-symmetric calculus operator theory and investigate a generalized symmetric Sălăgean q-differential operator for harmonic functions in an open unit disk. We consider a newly defined operator and establish new subclasses of harmonic functions in complex order. We determine the sharp results, such as the sufficient necessary coefficient bounds, the extreme of closed convex hulls, and the distortion theorems for a new family of harmonic functions. Further, we illustrate how we connect the findings of previous studies and the results of this article.

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.

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.

Subclass of Harmonic Univalent Functions Associated with the Generalized Mittag-Leffler Type Functions

In the present paper, we introduce a new subclass of harmonic functions in the unit disc U defined by using the generalized Mittag-Leffler type functions. Coefficient conditions, extreme points, distortion bounds, convex combination are studied.

Properties of Harmonic Functions Defined by Shear Construction

In this paper, we introduce a new subclass of harmonic functions defined by shear construction. Among other properties of this subclass, we study the convolution of its elements of it with some special subclasses of harmonic functions. Also, we provide coefficient conditions leading to harmonic mappings which are starlike of order \(\alpha \). Some interesting applications of the general results are also presented.

A Subclass of Harmonic Functions Related to a Convolution Operator

We introduce a new subclass of harmonic functions by using a certain linear operator. For this class we derive coefficient bounds, extreme points, and inclusion results and also show that this class is closed under an integral operator.

Special Subclasses of Harmonic Functions

Special Subclasses of Harmonic Functions

A subclass of harmonic functions with negative coefficients defined by Dziok-Srivastava operator

Making use of the Dziok-Srivastava operator, we introduce the class $% \mathcal{R}_{\overline{\mathcal{H}}}^{p,q}([\alpha _1],\lambda ,\gamma )$ of complex valued harmonic functions. We investigate the coefficient bounds, distortion inequalities , extreme points and inclusion results for this class.

A subclass of harmonic functions with negative coefficients defined by Dziok-Srivastava operator

Making use of the Dziok-Srivastava operator, we introduce the class $% \mathcal{R}_{\overline{\mathcal{H}}}^{p,q}([\alpha _1],\lambda ,\gamma )$ of complex valued harmonic functions. We investigate the coefficient bounds, distortion inequalities , extreme points and inclusion results for this class.

A subclass of harmonic functions with varying arguments defined by hypergeometric functions

We define the generalized Dziok-Srivastava operator for harmonic functions and introduce a new subclass of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc. We investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.

A New Subclass of Salagean‐Type Harmonic Univalent Functions

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

A Subclass of Harmonic Functions Associated with Wright’s Hypergeometric Functions

We introduce a new class of complex valued harmonic functions associated with Wright hypergeometric functions which are orientation preserving and univalent in the open unit disc. Further we define, Wright generalized operator on harmonic function and investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.

On Some Subclasses of Harmonic Functions Defined by Fractional Calculus

The purpose of this paper is to study subclasses of normalized harmonic functions with positive real part using fractional derivative. Sharp estimates for coefficients and distortion theorems are given.