Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means. (12th August 2010)

• Record Type: Journal Article
• Authors: Chu, Yu-Ming; Qiu, Ye-Fang; Wang, Miao-Kun
• Other Names: Littlejohn Lance Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2010(2010)
• Publication Date: 2010-08-12
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2010/108920
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We answer the question: forα ∈ ( 0, 1 ), what are the greatest valuep and the least valueq such that the double inequalityM p ( a, b ) < P α ( a, b ) G 1 − α ( a, b ) < M q ( a, b ) holds for alla, b > 0 witha ≠ b . Here, M p ( a, b ), P ( a, b ), andG ( a, b ) denote the power of orderp, Seiffert, and geometric means of two positive numbersa andb, respectively.