%0 Journal Article %A Menglong Su and Shaoyun Shi and Qing Xu %D 2012 %J International Journal of Mathematical and Computational Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 68, 2012 %T A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets %U https://publications.waset.org/pdf/11175 %V 68 %X In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper. %P 894 - 899