A continuation method for solving fixed points of self-mappings in general nonconvex sets
For the computation of fixed points of a sufficiently differentiable mapping from a non-convex, bounded subset \(\Omega \subset \mathbb{R}^n\) into itself, \textit{Z. Lin} and \textit{B. Yu} [Appl. Math. Comput. 74, 66-77 (1996; Zbl 0840.65038)] introduced a combined homotopy and interior-point method and proved for a class of sets \(\Omega\) that for almost all starting points, there exist regular solution curves of a specific homotopy which, in a certain sense, tend to the fixed point set. In this paper it is shown that the result remains valid under somewhat weakened conditions on the class of sets.
scientific article; zbMATH DE number 1879986