The Existence of Cone Critical Point and Common Fixed Point with Applications

We first establish some new critical point theorems for nonlinear dynamicalsystems in cone metric spaces or usual metric spaces, and then we present some applicationsto generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related withEkeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi'snonconvex minimization theorem, and common fuzzy fixed point theorem. We also obtainsome fixed point theorems for weakly contractive maps in the setting of cone metric spaces and focusour research on the equivalence between scalar versions and vectorial versions of some results of fixedpoint and others