Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Refinements of the Heinz inequalities | 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. Refinements of the Heinz inequalities Journal of Inequalities and Applications 2012 2012 18 doi 1029-242X-2012-18 Yuming Feng yumingfeng25928@ ISSN 1029-242X Article type Research Submission date 1 October 2011 Acceptance date 27 January 2012 Publication date 27 January 2012 Article URL http 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 authors instructions For information about other SpringerOpen publications go to http 2012 Feng licensee Springer. This is an open access article distributed under the terms of the Creative Commons Attribution License http licenses by which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1 Refinements of the Heinz inequalities Yuming Feng School of Mathematics and Statistics Chongqing Three Gorges University Wanzhou Chongqing 404100 . China Email address yumingfeng25928@ Abstract This article aims to discuss Heinz inequalities involving unitarily invariant norms. We obtain refinements of the Heinz inequalities. In particular our results refine some results given in Kittaneh. Keywords refinements Heinz inequality convex function Hermite-Hadamard inequality unitarily invariant norm. 1. Introduction If A B X are operators on a complex separable Hilbert space such that A and B are positive then for every unitarily invariant norm III III the function f v 111 AvXB v A 1 .
