The Existence of Cone Critical Point and Common Fixed Point with Applications. (25th October 2011)

• Record Type: Journal Article
• Authors: Du, Wei-Shih
• Other Names: Fang Ya Ping Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2011(2011)
• Publication Date: 2011-10-25
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2011/985797
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's nonconvex minimization theorem, and common fuzzy fixed point theorem. We also obtain some fixed point theorems for weakly contractive maps in the setting of cone metric spaces and focus our research on the equivalence between scalar versions and vectorial versions of some results of fixed point and others.