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 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 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 Convolutions of prestarlike functions

1983 ◽  
Vol 6 (1) ◽  
pp. 59-68 ◽  
Author(s):  
O. P. Ahuja ◽  
H. Silverman
Keyword(s):  
Unit Disk ◽  
Extremal Function ◽  
Extreme Points ◽  
Distortion Theorems ◽  
The Extremal Function ◽  
Class Of Functions

The convolution of two functionsf(z)=∑n=0∞anznandg(z)=∑n=0∞bnzndefined as(f∗g)(z)=∑n=0∞anbnzn. Forf(z)=z−∑n=2∞anznandg(z)=z/(1−z)2(1−γ), the extremal function for the class of functions starlike of orderγ, we investigate functionsh, whereh(z)=(f∗g)(z), which satisfy the inequality|(zh′/h)−1|/|(zh′/h)+(1-2α)|<β,0≤α<1,0<β≤1for allzin the unit disk. Such functionsfare said to beγ-prestarlike of orderαand typeβ. We characterize this family in terms of its coefficients, and then determine extreme points, distortion theorems, and radii of univalence, starlikeness, and convexity. All results are sharp.

On Janowski harmonic functions

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
Jacek Dziok
Keyword(s):  
Harmonic Functions ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Janowski Functions ◽  
Distortion Theorems ◽  
Necessary And Sufficient

AbstractIn this paper we define classes of harmonic functions related to the Janowski functions and we give some necessary and sufficient conditions for these classes. Some topological properties and extreme points of the classes are also considered. By using extreme points theory we obtain coefficients estimates, distortion theorems, integral mean inequalities for the classes of functions.

scholarly journals ON CERTAIN GENERALIZATIONS OF THE SPIRAL-LIKE AND ROBERTSON FUNCTIONS

1995 ◽  
Vol 26 (3) ◽  
pp. 201-223
Author(s):  
M. K. AOUF ◽  
H. E. ELATTAR
Keyword(s):  
Unit Disc ◽  
Coefficient Bounds ◽  
Representation Formulas ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Class C ◽  
Class Of Functions

Let $S^\lambda(\alpha, \beta, A, B)$ denote the class of functions $f(z)=z+\sum_{n=2}^\infty a_nz^n$ which are analytic in the unit disc $U=\{z:|z|<1\}$ and satisfy the inequality \[\left|\frac{F(z)}{(B-A)(F(z)+(1-\alpha)e^{-i\lambda}\cos \lambda)+AF(z)}\right|<1, \ \] where $F(z)=zf'(z)/f(z)-1$ for some $\lambda, \alpha, \beta, A, B$ ($|\lambda|<\pi/2, 0\le \alpha< 1, 0<\beta\le 1, -1\le A< B\le 1$ and $0<B\le 1$) and for all $z\in U$. Further $f(z)$ is said to belong to the class $C^\lambda(\alpha, \beta, A, B)$ ($|\lambda|<\pi/2, 0\le \alpha< 1, 0<\beta\le 1, -1\le A< B\le 1$ and $0<B\le 1$) if and only if $zf'(z) \in S^\lambda(\alpha, \beta, A, B)$. In the present paper, the authors give several representation formulas, distortion theorems, and coefficient bounds for functons belonging to these classes. They also obtain the sharp radius of $\gamma$-spiral and starlikeness for the class $S^\lambda(\alpha, \beta, A, B)$ and the sharp radius of $\gamma$-convex and convexity for the class $C^\lambda(\alpha, \beta, A, B)$.

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.

scholarly journals Properties of harmonic functions which are convex of order $ \bf \beta $ with respect to symmetric points

2009 ◽  
Vol 40 (1) ◽  
pp. 31-39 ◽  
Author(s):  
Aini Janteng ◽  
Suzeini Abdul Halim
Keyword(s):  
Unit Disc ◽  
Harmonic Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Symmetric Points ◽  
Complex Valued ◽  
Class Of Functions

Let $ \mathcal{H} $ denote the class of functions $ f $ which are harmonic and univalent in the open unit disc $ {D=\{z:|z|<1\}} $. This paper defines and investigates a family of complex-valued harmonic functions that are orientation preserving and univalent in $ \mathcal{D} $ and are related to the functions convex of order $ \beta(0\leq \beta <1) $, with respect to symmetric points. We obtain coefficient conditions, growth result, extreme points, convolution and convex combinations for the above harmonic functions.

scholarly journals Classes of harmonic functions defined by extended Sălăgean operator

2021 ◽  
Vol 73 (1) ◽  
pp. 33-46
Author(s):  
J. Dziok
Keyword(s):  
Harmonic Functions ◽  
Extreme Points ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Distortion Theorems

UDC 517.57 The object of the present paper is to investigate classes of harmonic functions defined by the extended Sălăgea operator. By using the extreme points theory we obtain coefficients estimates and distortion theorems for these classes of functions. Some integral mean inequalities are also pointed out.  

scholarly journals Classes of Harmonic Functions Defined by Subordination

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jacek Dziok
Keyword(s):  
Harmonic Functions ◽  
Extreme Points ◽  
Distortion Theorems

New classes of univalent harmonic functions are introduced. We give sufficient coefficient conditions for these classes. These coefficient conditions are shown to be also necessary if certain restrictions are imposed on the coefficients of these harmonic functions. By using extreme points theory we also obtain coefficients estimates, distortion theorems, and integral mean inequalities for these classes of functions. Radii of convexity and starlikeness of the classes are also considered.

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.

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