scholarly journals The Optimal Convex Combination Bounds of Arithmetic and Harmonic Means for the Seiffert's Mean

2010 ◽  
Vol 2010 (1) ◽  
pp. 436457 ◽  
Author(s):  
Yu-Ming Chu ◽  
Ye-Fang Qiu ◽  
Miao-Kun Wang ◽  
Gen-Di Wang
Keyword(s):  
Convex Combination ◽  
Harmonic Means

Sharp inequalities for bounding Seiffert mean in terms of the arithmetic, centroidal, and contra-harmonic means

2016 ◽  
Vol 66 (5) ◽  
Author(s):  
Wei-Dong Jiang ◽  
Jian Cao ◽  
Feng Qi
Keyword(s):  
Convex Combination ◽  
Parameter Family ◽  
Seiffert Mean ◽  
Second Seiffert Mean ◽  
Harmonic Means ◽  
The Second Seiffert Mean

AbstractIn the paper, the authors find two sharp and double inequalities for bounding the second Seiffert mean either by a one-parameter family of means derived from the centroidal mean or by a convex combination of the arithmetic and contra-harmonic means.

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

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