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 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 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 A Subclass of Harmonic Univalent Functions with Varying Arguments Defined by Generalized Derivative Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
E. A. Eljamal ◽  
M. Darus
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
New Class ◽  
Complex Valued ◽  
Class Of Functions ◽  
Varying Arguments

Making use of the generalized derivative operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and are related to uniformly convex functions. We investigate the coefficient bounds, neighborhood, and extreme points for this generalized class of functions.

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 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 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 Certain convex harmonic functions

2002 ◽  
Vol 29 (8) ◽  
pp. 459-465 ◽  
Author(s):  
Yong Chan Kim ◽  
Jay M. Jahangiri ◽  
Jae Ho Choi
Keyword(s):  
Analytic Functions ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Uniformly Convex ◽  
Coefficient Bounds ◽  
Distortion Theorems ◽  
Harmonic Convex ◽  
Complex Valued ◽  
Convex Univalent Functions

We define and investigate a family of complex-valued harmonic convex univalent functions related to uniformly convex analytic functions. We obtain coefficient bounds, extreme points, distortion theorems, convolution and convex combinations for this family.

scholarly journals On Certain Subclass of Harmonic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Distortion Bounds ◽  
Harmonic Starlike

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

scholarly journals Connections between Certain Subclasses of Analytic Univalent Functions Based on Operators

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
R. Ezhilarasi ◽  
T. V. Sudharsan ◽  
Maisarah Haji Mohd ◽  
K. G. Subramanian
Keyword(s):  
Linear Operator ◽  
Integral Operator ◽  
Hypergeometric Function ◽  
Analytic Functions ◽  
Univalent Functions

In this paper, by applying the Hohlov linear operator, connections between the class SD(α),  α≥0, and two subclasses of the class A of normalized analytic functions are established. Also an integral operator related to hypergeometric function is considered.

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