An Optimal Double Inequality between Seiffert and Geometric Means. (23rd November 2011)

• Record Type: Journal Article
• Authors: Chu, Yu-Ming; Wang, Miao-Kun; Wang, Zi-Kui
• Other Names: Butcher J. C. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2011(2011)
• Publication Date: 2011-11-23
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2011/261237
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : Forα, β ∈ ( 0, 1 / 2 ) we prove that the double inequalityG ( α a + ( 1 − α ) b, α b + ( 1 − α ) a ) < P ( a, b ) < G ( β a + ( 1 − β ) b, β b + ( 1 − β ) a ) holds for alla, b > 0 witha ≠ b if and only ifα ≤ ( 1 − 1 − 4 / π 2 ) / 2 andβ ≥ ( 3 − 3 ) / 6 . Here, G ( a, b ) andP ( a, b ) denote the geometric and Seiffert means of two positive numbersa andb, respectively.