Generalized trend constants of Lipschitz mappings

Mariusz Szczepanik

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2018)

  • Volume: 72, Issue: 2
  • ISSN: 0365-1029

Abstract

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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.

How to cite

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Mariusz Szczepanik. "Generalized trend constants of Lipschitz mappings." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 72.2 (2018): null. <http://eudml.org/doc/290757>.

@article{MariuszSzczepanik2018,
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.},
author = {Mariusz Szczepanik},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Banach space; Lipschitz mapping; fixed point},
language = {eng},
number = {2},
pages = {null},
title = {Generalized trend constants of Lipschitz mappings},
url = {http://eudml.org/doc/290757},
volume = {72},
year = {2018},
}

TY - JOUR
AU - Mariusz Szczepanik
TI - Generalized trend constants of Lipschitz mappings
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2018
VL - 72
IS - 2
SP - null
AB - 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.
LA - eng
KW - Banach space; Lipschitz mapping; fixed point
UR - http://eudml.org/doc/290757
ER -

References

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  1. Bolibok, K., Goebel, K., Trend constants for Lipschitz mappings, Fixed Point Theory 16 (2015), 215-224. 
  2. Da Prato, G., Zabczyk, J., Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992. 
  3. 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. 
  4. Ioffe, A. D., Tihomirov, V. M., Theory of Extremal Problems, North-Holland, Amsterdam, 1979. 
  5. Sato, K., On the generators of non-negative contraction semi-groups in Banach lattices, J. Math. Soc. Japan 20 (1968), 423-436. 

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