In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-6
Abstract:
We find the best possible constants α 1 , α 2 , β 1 , β 2 ∈ [ 0,1 / 2 ] and α 3 , α 4 , β 3 , β 4 ∈ [ 1 / 2,1 ] such that the double inequalities G ( α 1 a + ( 1 - α 1 ) b , α 1 b + ( 1 - α 1 ) a ) 〈 N A G ( a , b ) 〈 G ( β 1 a + ( 1 - β 1 ) b , β 1 b + ( 1 - β 1 ) a ) , G ( α 2 a + ( 1 - α 2 ) b , α 2 b + ( 1 - α 2 ) a ) 〈 N G A ( a , b ) 〈 G ( β 2 a + ( 1 - β 2 ) b , β 2 b + ( 1 - β 2 ) a ) , Q ( α 3 a + ( 1 - α 3 ) b , α 3 b + ( 1 - α 3 ) a ) 〈 N Q A ( a , b ) 〈 Q ( β 3 a + ( 1 - β 3 ) b , β 3 b + ( 1 - β 3 ) a ) , Q ( α 4 a + ( 1 - α 4 ) b , α 4 b + ( 1 - α 4 ) a ) 〈 N A Q ( a , b ) 〈 Q ( β 4 a + ( 1 - β 4 ) b , β 4 b + ( 1 - β 4 ) a ) hold for all a , b 〉 0 with a ≠ b , where G , A , and Q are, respectively, the geometric, arithmetic, and quadratic means and N A G , N G A , N Q A , and N A Q are the Neuman means.
Type of Medium:
Online Resource
ISSN:
1085-3375
,
1687-0409
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2014
detail.hit.zdb_id:
2064801-7
SSG:
17,1
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