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2011 The Existence of Cone Critical Point and Common Fixed Point with Applications
Wei-Shih Du
J. Appl. Math. 2011: 1-22 (2011). DOI: 10.1155/2011/985797


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.


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Wei-Shih Du. "The Existence of Cone Critical Point and Common Fixed Point with Applications." J. Appl. Math. 2011 1 - 22, 2011.


Published: 2011
First available in Project Euclid: 15 March 2012

zbMATH: 1304.54077
MathSciNet: MR2846436
Digital Object Identifier: 10.1155/2011/985797

Rights: Copyright © 2011 Hindawi


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