In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2011 ( 2011), p. 1-8
Abstract:
For p ∈ [ 0,1 ] , the generalized Seiffert mean of two positive numbers a and b is defined by S p ( a , b ) = p ( a - b ) / arctan [ 2 p ( a - b ) / ( a + b ) ] , 0 〈 p ≤ 1 , a ≠ b ; ( a + b ) / 2 , p = 0 , a ≠ b ; a , a = b . In this paper, we find the greatest value α and least value β such that the double inequality S α ( a , b ) 〈 T ( a , b ) 〈 S β ( a , b ) holds for all a , b 〉 0 with a ≠ b , and give new bounds for the complete elliptic integrals of the second kind. Here, T ( a , b ) = ( 2 / π ) ∫ 0 π / 2 a 2 cos 2 θ + b 2 sin 2 θ d θ denotes the Toader mean of two positive numbers a and b .
Type of Medium:
Online Resource
ISSN:
1085-3375
,
1687-0409
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2011
detail.hit.zdb_id:
2064801-7
SSG:
17,1
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