Fixed points of periodic mappings in Hilbert spaces

Victor Perez Garcia, Helga Fetter Nathansky

Abstract


In this paper we give new estimates for the Lipschitz constants of n-periodic mappings in Hilbert spaces, in order to assure the existence of fixed points and retractions on the fixed point set.

Keywords


Fixed point; retractions; periodic mappings

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References


Goebel, K., Kirk, W. A., Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990.

Goebel, K., Złotkiewicz, E., Some fixed point theorems in Banach spaces, Colloq. Math. 23 (1971), 103-106.

Górnicki, J., Pupka, K., Fixed points of rotative mappings in Banach spaces, J. Nonlinear Convex Anal. 6(2) (2005), 217-233.

Kaczor, W., Koter-Mórgowska M., Rotative mappings and mappings with constant displacement, Handbook of Metric Fixed Point Theory, Kluwer Academic Publisher, Dordrecht, 2001, 323-337.

Koter-Mórgowska, M., Rotative mappings in Hilbert space, J. Nonlinear Convex Anal. 1(3) (2000), 295-304.




DOI: http://dx.doi.org/10.2478/v10062-010-0013-y
Date of publication: 2016-07-29 10:39:55
Date of submission: 2016-07-28 22:14:54


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Copyright (c) 2010 Victor Perez Garcia, Helga Fetter Nathansky