Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan
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.
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 -functions. Some applications to the existence theorems of nonconvex versions of variational inclusion and disclusion problems
in metric spaces are also given.