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Zbl 1239.54017
Chen, Yong-Zhuo
A Prešić type contractive condition and its applications. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e-Suppl., e2012-e2017 (2009). ISSN 0362-546X

Summary: We study discrete dynamical systems in a complete metric space $(M, d)$ defined by mappings which satisfy Prešić type contractive conditions. Their counterparts in an ordered Banach space are investigated and applied to solve the global asymptotic stability of the equilibria of some nonlinear difference equations.

MSC 2000:: *54H20 Topological dynamics
39A30
47H07 Positive operators on ordered topological linear spaces

Keywords: cone; contractive condition; difference equation; metric space; ordered Banach space; Thompson's metric

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