scholarly journals On (p,q)-Starlike Harmonic Functions Defined By Subordination

2021 ◽  
Vol 26 (4) ◽  
pp. 491-500
Author(s):  
Hasan BAYRAM ◽  
Sibel Yalçın
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds ◽  
Necessary And Sufficient

We introduce and investigate classes of (p,q)-starlike 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 the (p,q)-starlike harmonic univalent with negative coefficients.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
A. T. Oladipo ◽  
D. Breaz
Keyword(s):  
Linear Operator ◽  
Harmonic Functions ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds

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.

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

2020 ◽  
pp. 139-153
Author(s):  
Adnan Ghazy Alamoush
Keyword(s):  
Unit Disc ◽  
Harmonic Functions ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds

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.

scholarly journals Subclasses of harmonic univalent functions associated with generalized Ruscheweyh operator

2019 ◽  
Vol 106 (120) ◽  
pp. 19-28
Author(s):  
Jacek Dziok ◽  
Sibel Yalçın ◽  
Şahsene Altınkaya
Keyword(s):  
Differential Operator ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Bounds ◽  
Distortion Bounds ◽  
Necessary And Sufficient

We introduce a new subclass of functions defined by multiplier differential operator and give coefficient bounds for these subclasses. Also, we obtain necessary and sufficient convolution conditions, distortion bounds and extreme points for these subclasses of functions.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Huda Aldweby ◽  
Maslina Darus
Keyword(s):  
Hypergeometric Function ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds ◽  
Basic Hypergeometric Function ◽  
Generalized Operator ◽  
Coefficient Condition ◽  
Necessary And Sufficient ◽  
Complex Valued

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.

scholarly journals A New Subclass of Salagean-Type Harmonic Univalent Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Khalifa Al-Shaqsi ◽  
Maslina Darus ◽  
Olubunmi Abidemi Fadipe-Joseph
Keyword(s):  
Harmonic Functions ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds

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.

scholarly journals A subclass of harmonic univalent functions with positive coefficients

2010 ◽  
Vol 41 (3) ◽  
pp. 261-269 ◽  
Author(s):  
K. K. Dixit ◽  
Saurabh Porwal
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Distortion Bounds ◽  
Positive Coefficients ◽  
Complex Valued

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disc $U$ can be written in the form $f=h+\bar g$, where $h$ and $g$ are analytic in $U$. In this paper authors introduce the class, $R_H(\beta)$, $(1<\beta \le 2)$ consisting of harmonic univalent functions $f=h+\bar g$, where $h$ and $g$ are of the form $ h(z)=z+ \sum_{k=2}^\infty |a_k|z^k $ and $ g(z)= \sum_{k=1}^\infty |b_k| z^k $ for which $\Re\{h'(z)+g'(z)\}<\beta$. We obtain distortion bounds extreme points and radii of convexity for 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 combinations.

scholarly journals Properties of a Class of -Harmonic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Elif Yaşar ◽  
Sibel Yalçın
Keyword(s):  
Differential Operator ◽  
Positive Integer ◽  
Harmonic Functions ◽  
Convex Combination ◽  
Extreme Points ◽  
Distortion Bounds ◽  
Harmonic Equation ◽  
Necessary And Sufficient ◽  
Complex Valued

A times continuously differentiable complex-valued function in a domain is -harmonic if satisfies the -harmonic equation , where is a positive integer. By using the generalized Salagean differential operator, we introduce a class of -harmonic functions and investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points, and convex combination of the class.

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

scholarly journals Harmonic univalent functions defined by post quantum calculus operators

2019 ◽  
Vol 11 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Om P. Ahuja ◽  
Asena Çetinkaya ◽  
V. Ravichandran
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Quantum Calculus ◽  
Special Cases ◽  
The Family ◽  
Covering Theorems

Abstract We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

Characterization of Extreme Points of Multi-Stochastic Tensors

2016 ◽  
Vol 16 (3) ◽  
pp. 459-474 ◽  
Author(s):  
Rihuan Ke ◽  
Wen Li ◽  
Mingqing Xiao
Keyword(s):  
Operation Research ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Stochastic Matrices ◽  
Third Order ◽  
New Approach ◽  
3 Dimensional ◽  
Necessary And Sufficient

AbstractStochastic matrices play an important role in the study of probability theory and statistics, and are often used in a variety of modeling problems in economics, biology and operation research. Recently, the study of tensors and their applications became a hot topic in numerical analysis and optimization. In this paper, we focus on studying stochastic tensors and, in particular, we study the extreme points of a set of multi-stochastic tensors. Two necessary and sufficient conditions for a multi-stochastic tensor to be an extreme point are established. These conditions characterize the “generators” of multi-stochastic tensors. An algorithm to search the convex combination of extreme points for an arbitrary given multi-stochastic tensor is developed. Based on our obtained results, some expression properties for third-order and n-dimensional multi-stochastic tensors (${n=3}$ and 4) are derived, and all extreme points of 3-dimensional and 4-dimensional triply-stochastic tensors can be produced in a simple way. As an application, a new approach for the partially filled square problem under the framework of multi-stochastic tensors is given.

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