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0 is considered and the corresponding result by G.D. Anderson, R.W. Barnard, K.C. Richards, M.K. Vamanamurthy and M. Vuorinen is generalized. As applications of these results, some inequalities between identric mean and ratio of two gamma functions by J.D. Kečkić and P.M. Vasić are extended.
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doi:10.1006/jmaa.1998.6104 
Copyright © 1998 Academic Press. All rights reserved.
Regular Article
Refinements and Extensions of an Inequality, III*1
Received 17 April 1998.
Available online 8 April 2002.
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Abstract
In this article, all of the cases of the inequality[formula]being or not being valid are discussed for all real numbersx, y 
andx ≠ 0, wherea, b > 0 anda ≠ b. Some recent developments concerning mean values are simply introduced.
Author Keywords: inequality; extended mean values; generalized weighted mean values; generalized weighted abstracted means; completely monotonic function; monotonicity; convexity; comparison
