Fixed points of multivalued contractions with nonclosed, nonconvex values

Salvatore A. Marano

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1994)

  • Volume: 5, Issue: 3, page 203-212
  • ISSN: 1120-6330

Abstract

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For a class of multivalued contractions with nonclosed, nonconvex values, the set of all fixed points is proved to be nonempty and arcwise connected. Two applications are then developed. In particular, one of them is concerned with some properties of the set of all classical trajectories corresponding to continuous controls for a given nonlinear control system.

How to cite

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Marano, Salvatore A.. "Fixed points of multivalued contractions with nonclosed, nonconvex values." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 5.3 (1994): 203-212. <http://eudml.org/doc/244199>.

@article{Marano1994,
abstract = {For a class of multivalued contractions with nonclosed, nonconvex values, the set of all fixed points is proved to be nonempty and arcwise connected. Two applications are then developed. In particular, one of them is concerned with some properties of the set of all classical trajectories corresponding to continuous controls for a given nonlinear control system.},
author = {Marano, Salvatore A.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Multivalued contraction; Fixed point; Arcwise connectedness; Nonlinear control system; arcwise connectedness; multivalued contractions; nonlinear control system},
language = {eng},
month = {9},
number = {3},
pages = {203-212},
publisher = {Accademia Nazionale dei Lincei},
title = {Fixed points of multivalued contractions with nonclosed, nonconvex values},
url = {http://eudml.org/doc/244199},
volume = {5},
year = {1994},
}

TY - JOUR
AU - Marano, Salvatore A.
TI - Fixed points of multivalued contractions with nonclosed, nonconvex values
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1994/9//
PB - Accademia Nazionale dei Lincei
VL - 5
IS - 3
SP - 203
EP - 212
AB - For a class of multivalued contractions with nonclosed, nonconvex values, the set of all fixed points is proved to be nonempty and arcwise connected. Two applications are then developed. In particular, one of them is concerned with some properties of the set of all classical trajectories corresponding to continuous controls for a given nonlinear control system.
LA - eng
KW - Multivalued contraction; Fixed point; Arcwise connectedness; Nonlinear control system; arcwise connectedness; multivalued contractions; nonlinear control system
UR - http://eudml.org/doc/244199
ER -

References

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  10. MICHAEL, E., Continuous selections I. Ann. of Math., 63, 1956, 361-382. Zbl0071.15902MR77107
  11. NASELLI RICCERI, O., A -fixed points of multi-valued contractions. J. Math. Anal. Appl., 135, 1988, 406-418. Zbl0662.54030MR967219DOI10.1016/0022-247X(88)90164-3
  12. NASELLI RICCERI, O., Classical solutions of the problem x ′ ∈ F ⁢ t , x , x ′ , x ⁢ t 0 = x 0 , x ′ ⁢ t 0 = y 0 in Banach spaces. Funkcial. Ekvac, 34, 1991, 127-141. Zbl0731.34071MR1116885
  13. RICCERI, B., Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes. Atti Acc. Lincei Rend. fis., s. 8, 81, 1987, 283-286. Zbl0666.47030MR999821
  14. ROBINSON, S. M., Normed convex processes. Trans. Amer. Math. Soc., 174, 1972, 127-140. Zbl0264.47018MR313769
  15. SAINT RAYMOND, J., Points fixes des contractions multivoques. In: J.-B. BAILLON - M. A. THÉRA (eds.), Fixed Point Theory and Applications (Marseille, 1989), Pitman Res. Notes Math. Ser., 252, Longman Sci. Tech., Harlow1991, 359-375. Zbl0757.47029MR1122843
  16. STAICU, V., Continuous flows of Lipschitzian differential inclusions. Preprint. 

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