scholarly journals Completely monotone sequences and harmonic mappings

2022 ◽  
Vol 47 (1) ◽  
pp. 237-250
Author(s):  
Bo-Yong Long ◽  
Toshiyuki Sugawa ◽  
Qi-Han Wang
Keyword(s):  
Harmonic Mappings ◽  
Geometric Properties ◽  
Monotone Sequences ◽  
Completely Monotone

In the present paper, we will study geometric properties of harmonic mappings whose analytic and co-analytic parts are (shifted) generated functions of completely monotone sequences.

Completely monotone sequences and universally prestarlike functions

2009 ◽  
Vol 171 (1) ◽  
pp. 285-304 ◽  
Author(s):  
Stephan Ruscheweyh ◽  
Luis Salinas ◽  
Toshiyuki Sugawa
Keyword(s):  
Monotone Sequences ◽  
Completely Monotone

scholarly journals Starlikeness, convexity and landau type theorem of the real kernel α-harmonic mappings

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2629-2644
Author(s):  
Bo-Yong Long ◽  
Qi-Han Wang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Type Theorem ◽  
Second Order ◽  
Harmonic Mappings ◽  
Partial Differential ◽  
Geometric Properties ◽  
The Real ◽  
Landau Type Theorem ◽  
Univalence Criteria

In [26], Olofsson introduced a kind of second order homogeneous partial differential equation. We call the solution of this equation real kernel ?-harmonic mappings. In this paper, we study some geometric properties of this real kernel ?-harmonic mappings. We give univalence criteria and sufficient coefficient conditions for real kernel ?-harmonic mappings that are fully starlike or fully convex of order ?, ? ? [0, 1). Furthermore, we establish a Landau type theorem for real kernel ?-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.

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