scholarly journals A Convex Combination of Two-Sample U-Statistics

2006 ◽  
Vol 36 (1) ◽  
pp. 73-89
Author(s):  
Koichiro Toda ◽  
Hajime Yamato
Keyword(s):  
Convex Combination ◽  
U Statistics

scholarly journals AN EDGEWORTH EXPANSION OF A CONVEX COMBINATION OF U-STATISTICS BASED ON STUDENTIZATION

10.5109/12582 ◽  
2004 ◽  
Vol 36 ◽  
pp. 105-130
Author(s):  
Hajime Yamato ◽  
Koichiro Toda ◽  
Toshifumi Nomachi ◽  
Yoshihiko Maesono
Keyword(s):  
Edgeworth Expansion ◽  
Convex Combination ◽  
U Statistics

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 $\overline{HS}(k,\lambda,b,\alpha)$.

Sign in / Sign up

Export Citation Format

Share Document