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

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  • Dongjie Gao

Abstract

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.

Suggested Citation

  • Dongjie Gao, 2015. "A Fixed Point Theorem for Monotone Maps and Its Applications to Nonlinear Matrix Equations," Journal of Mathematics, Hindawi, vol. 2015, pages 1-6, December.
    • Handle: RePEc:hin:jjmath:167049
    DOI: 10.1155/2015/167049
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