scholarly journals The function (bx−ax)/x: Logarithmic convexity and applications to extended mean values

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 63-73 ◽  
Author(s):  
Bai-Ni Guo ◽  
Qi Feng
Keyword(s):  
Simple Proof ◽  
Elementary Function ◽  
Logarithmic Convexity ◽  
Mean Values ◽  
Schur Convex ◽  
Extended Mean Values

In the paper, we first prove the logarithmic convexity of the elementary function bx?ax/x, where x ? 0 and b > a > 0. Basing on this, we then provide a simple proof for Schur-convex properties of the extended mean values, and, finally, discover some convexity related to the extended mean values.

Corrections to "Extended Mean Values"

1978 ◽  
Vol 85 (8) ◽  
pp. 656
Author(s):  
E. B. Leach ◽  
M. C. Sholander
Keyword(s):  
Mean Values ◽  
Extended Mean Values

scholarly journals A new proof of monotonicity for extended mean values

1999 ◽  
Vol 22 (2) ◽  
pp. 417-421 ◽  
Author(s):  
Feng Qi ◽  
Sen-Lin Xu ◽  
Lokenath Debnath
Keyword(s):  
Mean Values ◽  
Extended Mean Values

In this article, a new proof of monotonicity for extended mean values is given.

scholarly journals Multi-variable extended mean values

1984 ◽  
Vol 104 (2) ◽  
pp. 390-407 ◽  
Author(s):  
E.B Leach ◽  
M.C Sholander
Keyword(s):  
Mean Values ◽  
Extended Mean Values

scholarly journals Another proof of monotonicity for extended mean values

2006 ◽  
Vol 37 (3) ◽  
pp. 207-209
Author(s):  
Su-Ling Zhang ◽  
Chao-Ping Chen ◽  
Feng Qi
Keyword(s):  
Mean Values ◽  
Extended Mean Values

We provide another proof of monotonicity for the extended mean values.

scholarly journals SCHUR-GEOMETRIC CONVEXITY OF STOLARSKY'S EXTENDED MEAN VALUES

2017 ◽  
Vol 114 (1) ◽  
Author(s):  
R.C.L. Janardhana ◽  
K.M. Nagaraja ◽  
V. Lokesha
Keyword(s):  
Mean Values ◽  
Extended Mean Values

Corrections to “Extended Mean Values”

1978 ◽  
Vol 85 (8) ◽  
pp. 656-656
Author(s):  
E. B. Leach ◽  
M. C. Sholander
Keyword(s):  
Mean Values ◽  
Extended Mean Values
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