Abstract
AbstractIn this study, both theoretical results and numerical methods are derived for solving different classes of systems of nonlinear matrix equations involving Lipshitzian mappings.2000 Mathematics Subject Classifications: 15A24; 65H05.
Highlights
Fixed point theory is a very attractive subject, which has recently drawn much attention from the communities of physics, engineering, mathematics, etc
Both theoretical results and numerical methods are derived for solving different classes of systems of nonlinear matrix equations involving Lipshitzian mappings. 2000 Mathematics Subject Classifications: 15A24; 65H05
The Thompson metric exists on any open normal convex cones of real Banach spaces [5,6]; in particular, the open convex cone of positive definite operators of a Hilbert space
Summary
Fixed point theory is a very attractive subject, which has recently drawn much attention from the communities of physics, engineering, mathematics, etc. The Banach contraction principle [1] is one of the most important theorems in fixed point theory. The Thompson metric exists on any open normal convex cones of real Banach spaces [5,6]; in particular, the open convex cone of positive definite operators of a Hilbert space. It is invariant under the matrix inversion and congruence transformations, that is, d(A, B) = d(A−1, B−1) = d(MAM∗, MBM∗). Applying the Banach contraction principle (see Theorem 1.1) to the mapping G, we get the desired result.
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