Abstract and Applied Analysis
Volume 2010 (2010), Article ID 108920, 12 pages
doi:10.1155/2010/108920
Research Article

Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means

Yu-Ming Chu,1 Ye-Fang Qiu,2 and Miao-Kun Wang2

1Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
2Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received 29 March 2010; Revised 23 July 2010; Accepted 29 July 2010

Academic Editor: Lance Littlejohn

Copyright © 2010 Yu-Ming Chu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We answer the question: for α∈(0,1), what are the greatest value p and the least value q such that the double inequality Mp(a,b)<Pα(a,b)G1−α(a,b)<Mq(a,b) holds for all a,b>0 with a≠b. Here, Mp(a,b), P(a,b), and G(a,b) denote the power of order p, Seiffert, and geometric means of two positive numbers a and b, respectively.