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Abstract and Applied Analysis
Volume 2014, Article ID 457367, 7 pages
http://dx.doi.org/10.1155/2014/457367
Research Article

Some Properties of Furuta Type Inequalities and Applications

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454000, China

Received 25 January 2014; Accepted 20 March 2014; Published 13 April 2014

Academic Editor: Changsen Yang

Copyright © 2014 Jiangtao Yuan and Caihong Wang. 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

This work is to consider Furuta type inequalities and their applications. Firstly, some Furuta type inequalities under are obtained via Loewner-Heinz inequality; as an application, a proof of Furuta inequality is given without using the invertibility of operators. Secondly, we show a unified satellite theorem of grand Furuta inequality which is an extension of the results by Fujii et al. At the end, a kind of Riccati type operator equation is discussed via Furuta type inequalities.