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Báo cáo toán học: " Sharp bounds for Seiffert mean in terms of root mean square"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Sharp bounds for Seiffert mean in terms of root mean square | Journal of Inequalities and Applications SpringerOpen0 This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text HTML versions will be made available soon. Sharp bounds for Seiffert mean in terms of root mean square Journal of Inequalities and Applications 2012 2012 11 doi 10.1186 1029-242X-2012-11 Yu-Ming Chu chuyuming2005@yahoo.com.cn Shou-Wei Hou houshouwei2008@163.com Zhong-Hua Shen ahtshen@126.com ISSN 1029-242X Article type Research Submission date 19 September 2011 Acceptance date 17 January 2012 Publication date 17 January 2012 Article URL http www.journalofinequalitiesandapplications.com content 2012 1 This peer-reviewed article was published immediately upon acceptance. It can be downloaded printed and distributed freely for any purposes see copyright notice below . For information about publishing your research in Journal of Inequalities and Applications go to http www.journalofinequalitiesandapplications.com authors instructions For information about other SpringerOpen publications go to http www.springeropen.com 2012 Chu etal. licensee Springer. This is an open access article distributed under the terms of the Creative Commons Attribution License http creativecommons.org licenses by 2.0 which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Sharp bounds for Seiffert mean in terms of root mean square Yu-Ming Chu 1 Shou-Wei Hou2 and Zhong-Hua Shen2 Department of Mathematics Huzhou Teachers College Huzhou 313000 China 2Department of Mathematics Hangzhou Normal University Hangzhou 310012 China Corresponding author chuyuming2005@yahoo.com.cn Email addresses S-WH houshouwei2008@163.com Z-HS ahtshen@126.com Abstract We find the greatest value a and least value 3 in 1 2 1 such that the double inequality S aa 1 a b ab 1 a a T a b S 3a 1 3 b 3b 1 3 a 1 holds for all a b 0 with a b. Here T a b a b 2 arctan a b a b and S a b a2 b2 2 x 2 are the