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Journal of Mathematics
Volume 2015, Article ID 167049, 6 pages
Research Article

A Fixed Point Theorem for Monotone Maps and Its Applications to Nonlinear Matrix Equations

Department of Mathematics, Heze University, Heze, Shandong 274015, China

Received 25 July 2015; Revised 27 October 2015; Accepted 23 November 2015

Academic Editor: Frank Uhlig

Copyright © 2015 Dongjie Gao. 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.


By using the fixed point theorem for monotone maps in a normal cone, we prove a uniqueness theorem for the positive definite solution of the matrix equation , where is a monotone map on the set of positive definite matrices. Then we apply the uniqueness theorem to a special equation and prove that the equation has a unique positive definite solution when and and . For this equation the basic fixed point iteration is discussed. Numerical examples show that the iterative method is feasible and effective.