Copyright © 2010 Wei-Shih Du. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present some new critical point theorems for nonlinear dynamical systems which are generalizations of Dancš-Hegedüs-Medvegyev's principle in uniform spaces and metric spaces by applying an abstract maximal element principle established by Lin and Du. We establish some generalizations of Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's nonconvex minimization theorem, and common fuzzy fixed point theorem for τ-functions. Some applications to the existence theorems of nonconvex versions of variational inclusion and disclusion problems in metric spaces are also given.