Abstract and Applied Analysis
Volume 2009 (2009), Article ID 694394, 10 pages
doi:10.1155/2009/694394

Optimal inequalities among various means of two arguments

Ming-Yu Shi1 , Yu-Ming Chu2 and Yue-Ping Jiang1

1College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
 2Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

Abstract

We establish two optimal inequalities among power mean Mp(a,b)=(ap/2+bp/2)1/p, arithmetic mean A(a,b)=(a+b)/2, logarithmic mean L(a,b)=(a−b)/(log⁡a−log⁡b), and geometric mean G(a,b)=ab.