scholarly journals The Bohr inequality for certain harmonic mappings

2021 ◽  
Author(s):  
Vasudevarao Allu ◽  
Himadri Halder
Keyword(s):  
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 $\overline{HS}(k,\lambda,b,\alpha)$.

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.

On subclasses of harmonic mappings involving Frasin operator

2021 ◽  
Author(s):  
Muhammad G. Khan ◽  
Bakhtiar Ahmad ◽  
Zabidin Salleh ◽  
Iing Lukman
Keyword(s):  
Harmonic Mappings

Bohr radius for certain classes of close-to-convex harmonic mappings

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Molla Basir Ahamed ◽  
Vasudevarao Allu ◽  
Himadri Halder
Keyword(s):  
Harmonic Mappings ◽  
Bohr Radius

scholarly journals On the univalence of certain integral for harmonic mappings

2017 ◽  
Vol 455 (1) ◽  
pp. 381-388 ◽  
Author(s):  
Víctor Bravo ◽  
Rodrigo Hernández ◽  
Osvaldo Venegas
Keyword(s):  
Harmonic Mappings

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

Bounded harmonic mappings

2010 ◽  
Vol 111 (1) ◽  
pp. 47-76 ◽  
Author(s):  
Wojciech Szapiel
Keyword(s):  
Harmonic Mappings

On the Volume Decreasing Property of a Class of Real Harmonic Mappings

1975 ◽  
Vol 97 (1) ◽  
pp. 133 ◽  
Author(s):  
Shiing-shen Chern ◽  
Samuel I. Goldberg
Keyword(s):  
Harmonic Mappings

scholarly journals Improved Bohr’s inequality for locally univalent harmonic mappings

2019 ◽  
Vol 30 (1) ◽  
pp. 201-213 ◽  
Author(s):  
Stavros Evdoridis ◽  
Saminathan Ponnusamy ◽  
Antti Rasila
Keyword(s):  
Harmonic Mappings ◽  
Bohr’S Inequality ◽  
Univalent Harmonic Mappings
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