scholarly journals A Subclass of Harmonic Functions Related to a Convolution Operator

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Saqib Hussain ◽  
Akhter Rasheed ◽  
Maslina Darus
Keyword(s):  
Linear Operator ◽  
Integral Operator ◽  
Convolution Operator ◽  
Harmonic Functions ◽  
Extreme Points ◽  
Coefficient Bounds ◽  
Inclusion Results

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.

scholarly journals Harmonic functions of class of Bazilevi´c type Related to new derivative operator

2019 ◽  
Vol 30 (1) ◽  
pp. 125 ◽  
Author(s):  
Abdul Rahman S. Juma ◽  
Mushtaq S. Abdulhussain ◽  
Saba Nazar Al-khafaji
Keyword(s):  
Linear Operator ◽  
Integral Operator ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Distortion Bound

In this paper, we define and investigate subclass of Bazilevi´c type harmonic univalent functions related with a new linear operator. Also, we have obtained the harmonic structures in terms of its coefficient bounds, extreme points, distortion bound, convolution and we proved the function belongs to this class be closed under an integral operator.

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

2011 ◽  
Vol 42 (4) ◽  
pp. 463-473
Author(s):  
G. Murugusundaramoorthy ◽  
K. Vijaya ◽  
Basem Aref Frasin
Keyword(s):  
Harmonic Functions ◽  
Extreme Points ◽  
Coefficient Bounds ◽  
Complex Valued ◽  
Inclusion Results

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.

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 Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator

2021 ◽  
pp. 49-76
Author(s):  
Faroze Ahmad Malik ◽  
Nusrat Ahmed Dar ◽  
Chitaranjan Sharma
Keyword(s):  
Convex Functions ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Extreme Points ◽  
Integral Operators ◽  
Integral Means ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Special Cases ◽  
The Family

We use the concept of convolution to introduce and study the properties of a unified family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$, $(0\leq\gamma\leq1,\,k\geq0)$, consisting of uniformly $k$-starlike and $k$-convex functions of complex order $b\in\mathbb{C}\setminus\{0\}$ and type $\alpha\in[0,1)$. The family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$ is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman's conjecture for integral means inequality. Moreover, invariance of this family under certain well-known integral operators is also established in this paper. Some previously known results are obtained as special cases.

scholarly journals A NEW SUBCLASS OF STARLIKE HARMONIC FUNCTIONS DEFINED BY SUBORDINATION

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Serkan Çakmak ◽  
Sibel Yalçın ◽  
Şahsene Altınkaya
Keyword(s):  
Harmonic Functions ◽  
Extreme Points ◽  
Current Work ◽  
Coefficient Bounds ◽  
Distortion Theorems ◽  
Class Of Functions

In this current work, by using a relation of subordination, we define a new subclass of starlike harmonic functions. We get coefficient bounds, distortion theorems, extreme points, convolution and convex combinations for this class of functions. Moreover, some relevant connections of the results presented here with diverse known results are briefly denoted.

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.

A New Subclass of Harmonic Univalent Functions

2017 ◽  
Vol 9 (2) ◽  
pp. 26-32
Author(s):  
Waggas Galib Atshan ◽  
Najah Ali Jiben Al-Ziadi
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Basic Properties ◽  
New Class

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.

scholarly journals Some Properties of a Class of Harmonic Multivalent Functions Defined by an Integral Operator

2019 ◽  
Vol 27 (2) ◽  
pp. 261-268
Author(s):  
Aqeel Ketab AL-khafaji ◽  
Waggas Galib Atshan ◽  
Salwa Salman Abed
Keyword(s):  
Integral Operator ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Inclusion Results

Some properties of a class of harmonic multivalent functions defined by an integral operator are introduced, like, coefficient estimates, distortion property, extreme points, inclusion results and  closure under an integral operator for this class are obtained.

scholarly journals Classes of meromorphic harmonic functions and duality principle

2020 ◽  
Vol 10 (4) ◽  
Author(s):  
Jacek Dziok
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Duality Principle ◽  
Coefficient Bounds

AbstractWe introduce new classes of meromorphic harmonic univalent functions. Using the duality principle, we obtain the duals of such classes of functions leading to coefficient bounds, extreme points and some applications for these functions.

scholarly journals On a Subclass of Harmonic Convex Functions of Complex Order

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
N. Magesh ◽  
S. Mayilvaganan
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Convex Combination ◽  
Extreme Points ◽  
Closure Property ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Distortion Bounds ◽  
Order Coefficient ◽  
Harmonic Convex

We introduce and study a subclass of harmonic convex functions of complex order. Coefficient bounds, extreme points, distortion bounds, convolution conditions, and convex combination are determined for functions in this class. Further, we obtain the closure property of this class under integral operator.

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