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

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.