Harmonic mappings related to the m-fold starlike functions

2015 ◽  
Vol 267 ◽  
pp. 805-809
Author(s):  
Melike Aydoğan ◽  
Yaşar Polatoğlu ◽  
Yasemin Kahramaner
Keyword(s):  
Starlike Functions ◽  
Harmonic Mappings

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 mappings related to Janowski starlike functions

2014 ◽  
Vol 270 ◽  
pp. 564-570
Author(s):  
Yasemin Kahramaner ◽  
Yaşar Polatog˜lu ◽  
Melike Aydog˜an
Keyword(s):  
Starlike Functions ◽  
Harmonic Mappings

scholarly journals Bounded harmonic mappings related to starlike functions

2014 ◽  
Author(s):  
Durdane Varol ◽  
Melike Aydoğan ◽  
Yaşar Polatoğlu
Keyword(s):  
Starlike Functions ◽  
Harmonic Mappings

scholarly journals The Generalized Janowski Starlike and Close-to-Starlike Log-Harmonic Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Maisarah Haji Mohd ◽  
Maslina Darus
Keyword(s):  
Unit Disc ◽  
Harmonic Mapping ◽  
Starlike Functions ◽  
Starlike Function ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disc

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form defined on the open unit disc . The functions are in the class of the generalized Janowski starlike log-harmonic mapping, , with the functional in the class of the generalized Janowski starlike functions, . By means of these functions, we obtained results on the generalized Janowski close-to-starlike log-harmonic mappings, .

scholarly journals Quasiconformal Harmonic Mappings Related to Janowski Starlike Functions

2014 ◽  
Vol 43 (12) ◽  
pp. 1961-1964
Author(s):  
Yasemin Kahramaner ◽  
Yaşar Polatoğlu
Keyword(s):  
Starlike Functions ◽  
Harmonic Mappings

scholarly journals The Distortion Theorems for Harmonic Mappings with Analytic Parts Convex or Starlike Functions of Orderβ

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Mengkun Zhu ◽  
Xinzhong Huang
Keyword(s):  
Starlike Functions ◽  
Harmonic Mappings ◽  
Sharp Estimates ◽  
Covering Theorems ◽  
Distortion Theorems

Some sharp estimates of coefficients, distortion, and growth for harmonic mappings with analytic parts convex or starlike functions of orderβare obtained. We also give area estimates and covering theorems. Our main results generalise those of Klimek and Michalski.

On λ-pseudo bi-starlike functions related to some conic domains

2020 ◽  
Vol 61(12) (2) ◽  
pp. 381-392
Author(s):  
Gangadhara Murugusundaramoorthy ◽  
◽  
Janusz Sokol ◽  
Keyword(s):  
Starlike Functions

On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

2020 ◽  
pp. 445-454
Author(s):  
Deepali Khurana ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Imaginary Axis ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Distortion Bounds ◽  
Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*

2020 ◽  
Vol 70 (4) ◽  
pp. 849-862
Author(s):  
Shagun Banga ◽  
S. Sivaprasad Kumar
Keyword(s):  
Triangle Inequality ◽  
Starlike Functions ◽  
Sharp Bound ◽  
The Novel ◽  
Sharp Bounds ◽  
Hankel Determinants ◽  
Lemniscate Of Bernoulli ◽  
Carathéodory Functions ◽  
The Right

AbstractIn this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H3(1) and H2(3) for the well known class 𝓢𝓛* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: $\begin{array}{} |a_3^2-a_5| \end{array}$ for the class 𝓢𝓛* is also estimated. Further, a couple of interesting results of 𝓢𝓛* are also discussed.

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