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We consider a class of nonlinear matrix equations of the form X n − f (X) = 0 where f is a self-map on the convex cone P (k) of k × k positive definite real matrices. It is shown that for n ≥ 2, the matrix equation has a unique positive definite solution if f belongs to the semigroup of nonexpansive mappings with respect to the GL(k, R)-invariant Riemannian… (More)

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