Generalized trend constants of Lipschitz mappings

Mariusz Szczepanik

Abstract


In 2015, Goebel and Bolibok defined the initial trend coefficient of a mapping and the class of initially nonexpansive mappings. They proved that the fixed point property for nonexpansive mappings implies the fixed point property for initially nonexpansive mappings. We generalize the above concepts and prove an analogous fixed point theorem. We also study the initial trend coefficient more deeply.

Keywords


Banach space; Lipschitz mapping; fixed point

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References


Bolibok, K., Goebel, K., Trend constants for Lipschitz mappings, Fixed Point Theory 16 (2015), 215-224.

Da Prato, G., Zabczyk, J., Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.

Goebel, K., Minimal displacement and trend constants for Lipschitz mappings, in: Proceedings of the 9th International Conference on Nonlinear Analysis and Convex Analysis, (2016), 111-121.

Ioffe, A. D., Tihomirov, V. M., Theory of Extremal Problems, North-Holland, Amsterdam, 1979.

Sato, K., On the generators of non-negative contraction semi-groups in Banach lattices, J. Math. Soc. Japan 20 (1968), 423-436.




DOI: http://dx.doi.org/10.17951/a.2018.72.2.71
Date of publication: 2018-12-22 22:03:14
Date of submission: 2018-12-21 23:13:15


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