In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2010 ( 2010), p. 1-13
Abstract:
We answer the question: for α , β , γ ∈ ( 0,1 ) with α + β + γ = 1 , what are the greatest value p and the least value q , such that the double inequality L p ( a , b ) 〈 A α ( a , b ) G β ( a , b ) H γ ( a , b ) 〈 L q ( a , b ) holds for all a , b 〉 0 with a ≠ b ? Here L p ( a , b ) , A ( a , b ) , G ( a , b ) , and H ( a , b ) denote the generalized logarithmic, arithmetic, geometric, and harmonic means of two positive numbers a and b , respectively.
Type of Medium:
Online Resource
ISSN:
1085-3375
,
1687-0409
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2010
detail.hit.zdb_id:
2064801-7
SSG:
17,1
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