Optimal Lehmer Mean Bounds for the Combinations of Identric and Logarithmic Means. (10th September 2013)

• Record Type: Journal Article
• Authors: Shen, Xu-Hui; Gong, Wei-Ming; Chu, Yu-Ming
• Other Names: Coppens M. Academic Editor.; Miao Y. Academic Editor.; Nie P.-y. Academic Editor.
• Is Part Of: Chinese journal of mathematics. Volume 2013(2013)
• Publication Date: 2013-09-10
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals
• DOI: 10.1155/2013/852516
• Languages: English
• ISSNs: 2314-8071

Abstract

Abstract : For anyα ∈ 0, 1, we answer the questions: what are the greatest valuesp andλ and the least valuesq andμ, such that the inequalitiesL p a, b < I α a, b L 1 - α a, b < L q a, b andL λ a, b < α I a, b + 1 - α L a, b < L μ a, b hold for alla, b > 0 witha ≠ b ? Here, I a, b, L a, b, andL p a, b denote the identric, logarithmic, andp th Lehmer means of two positive numbersa andb, respectively.