A boundary perturbation interior point homotopy method for solving fixed point problems

In this paper, a boundary perturbation interior point homotopy method is proposed to give a constructive proof of the general Brouwer fixed point theorem and thus solve fixed point problems in a class of nonconvex sets. Compared with the previous results, by using the newly proposed method, initial points can be chosen in the whole space of R n , which may improve greatly the computational efficiency of reduced predictor–corrector algorithms resulted from that method. Some numerical examples are given to illustrate the results of this paper.