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 Monotonicity of the Ratio of the Power and Second Seiffert Means with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Zhen-Hang Yang ◽  
Ying-Qing Song ◽  
Yu-Ming Chu
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Power Mean ◽  
Seiffert Mean ◽  
Second Seiffert Mean ◽  
Necessary And Sufficient ◽  
The Second Seiffert Mean

We present the necessary and sufficient condition for the monotonicity of the ratio of the power and second Seiffert means. As applications, we get the sharp upper and lower bounds for the second Seiffert mean in terms of the power mean.

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

scholarly journals Optimal Two Parameter Bounds for the Seiffert Mean

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Hui Sun ◽  
Ying-Qing Song ◽  
Yu-Ming Chu
Keyword(s):  
Parameter Family ◽  
Sharp Bounds ◽  
Seiffert Mean ◽  
Two Parameter ◽  
Parameter Bounds

We obtain sharp bounds for the Seiffert mean in terms of a two parameter family of means. Our results generalize and extend the recent bounds presented in the Journal of Inequalities and Applications (2012) and Abstract and Applied Analysis (2012).

Sign in / Sign up

Export Citation Format

Share Document