Modified homotopy methods to solve fixed points of self-mapping in a broader class of nonconvex sets

Authors:
Menglong Su;Zhenxin Liu
Affiliations:
Mathematics and Information Science College, Luoyang Normal University, Luoyang 471022, PR China and College of Mathematics, Jilin University, Changchun 130012, PR China;College of Mathematics, Jilin University, Changchun 130012, PR China
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

This paper consists of two parts. In Section 2, we are mainly devoted to modify a combined homotopy interior point method (proposed by Yu and Lin, Homotopy method for a class of nonconvex Brouwer fixed point problems, Appl. Math. Comput. 74 (1996) 65-77) to solve fixed points of self-mapping in a broader class of nonconvex sets. Several numerical examples are presented to show the effectiveness of modifications. In Section 3, we modify their method to solve fixed points of self-mapping in the unbounded convex sets, a simple example is given to show its modification.