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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 8901258, 7 pages
http://dx.doi.org/10.1155/2016/8901258
Research Article

Best Possible Bounds for Yang Mean Using Generalized Logarithmic Mean

1School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, China
2Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

Received 23 January 2016; Revised 16 March 2016; Accepted 28 March 2016

Academic Editor: Kishin Sadarangani

Copyright © 2016 Wei-Mao Qian and Yu-Ming Chu. 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 prove that the double inequality holds for all with if and only if and and find several sharp inequalities involving the trigonometric, hyperbolic, and inverse trigonometric functions, where is the unique solution of the equation on the interval , , and , and are the Yang, and th generalized logarithmic means of and , respectively.