scholarly journals Quasiconformal extension for harmonic mappings on finitely connected domains

2021 ◽  
Vol 359 (7) ◽  
pp. 905-909
Author(s):  
Iason Efraimidis
Keyword(s):  
Quasiconformal Extension ◽  
Harmonic Mappings

scholarly journals Quasiconformal extension of harmonic mappings in the plane

2013 ◽  
Vol 38 ◽  
pp. 617-630 ◽  
Author(s):  
Rodrigo Hernández ◽  
María J. Martín
Keyword(s):  
Quasiconformal Extension ◽  
Harmonic Mappings

scholarly journals Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative

2014 ◽  
Vol 104 (1) ◽  
pp. 53-59 ◽  
Author(s):  
Rodrigo Hernández ◽  
María J. Martín
Keyword(s):  
Schwarzian Derivative ◽  
Quasiconformal Extension ◽  
Harmonic Mappings

Criteria for univalency and quasiconformal extension for harmonic mappings

2021 ◽  
Vol 44 (2) ◽  
Author(s):  
Zhenyong Hu ◽  
Jinhua Fan
Keyword(s):  
Quasiconformal Extension ◽  
Harmonic Mappings

QUASICONFORMAL EXTENSIONS OF HARMONIC MAPPINGS WITH A COMPLEX PARAMETER

2016 ◽  
Vol 102 (3) ◽  
pp. 307-315 ◽  
Author(s):  
XINGDI CHEN ◽  
YUQIN QUE
Keyword(s):  
Analytic Functions ◽  
Extension Theorem ◽  
Sufficient Conditions ◽  
Complex Parameter ◽  
Quasiconformal Extension ◽  
Harmonic Mappings ◽  
Maximal Dilatation ◽  
The One ◽  
Teichmüller Mapping

In this paper, we study quasiconformal extensions of harmonic mappings. Utilizing a complex parameter, we build a bridge between the quasiconformal extension theorem for locally analytic functions given by Ahlfors [‘Sufficient conditions for quasiconformal extension’, Ann. of Math. Stud.79 (1974), 23–29] and the one for harmonic mappings recently given by Hernández and Martín [‘Quasiconformal extension of harmonic mappings in the plane’, Ann. Acad. Sci. Fenn. Math.38 (2) (2013), 617–630]. We also give a quasiconformal extension of a harmonic Teichmüller mapping, whose maximal dilatation estimate is asymptotically sharp.

scholarly journals Criteria for univalence and quasiconformal extension for harmonic mappings on planar domains

2021 ◽  
Vol 46 (2) ◽  
pp. 1123-1134
Author(s):  
Iason Efraimidis
Keyword(s):  
Quasiconformal Extension ◽  
Harmonic Mappings ◽  
Planar Domains

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
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