scholarly journals Optimal bounds for Neuman-Sándor mean in terms of the convex combination of logarithmic and quadratic or contra-harmonic means

2014 ◽  
pp. 201-217 ◽  
Author(s):  
Yuming Chu ◽  
Tie-Hong Zhao ◽  
Baoyu Liu
Keyword(s):  
Convex Combination ◽  
Optimal Bounds ◽  
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.

scholarly journals Optimal Bounds for the Neuman-Sándor Mean in terms of the Convex Combination of the First and Second Seiffert Means

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Hao-Chuan Cui ◽  
Nan Wang ◽  
Bo-Yong Long
Keyword(s):  
Convex Combination ◽  
Double Inequality ◽  
Optimal Bounds

We find the least valueαand the greatest valueβsuch that the double inequalityαP(a,b)+(1-α)T(a,b)<M(a,b)<βP(a,b)+(1-β)T(a,b)holds for alla,b>0witha≠b, whereM(a,b), P(a,b), andT(a,b)are the Neuman-Sándor mean and the first and second Seiffert means of two positive numbersaandb, respectively.

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
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