Continuous dependence on parameters of the fixed points set for some set-valued operators
Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1997)
- Volume: 17, Issue: 1-2, page 29-41
- ISSN: 1509-9407
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topEduard Kirr, and Adrian Petruel. "Continuous dependence on parameters of the fixed points set for some set-valued operators." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 17.1-2 (1997): 29-41. <http://eudml.org/doc/275885>.
@article{EduardKirr1997,
abstract = {In this paper we extend the notion of I⁰-continuity and uniform I⁰-continuity from [2] to set-valued operators. Using these properties, we prove some results on continuous dependence of the fixed points set for families of contractive type set-valued operators.},
author = {Eduard Kirr, Adrian Petruel},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {I⁰-continuity; semi-continuous set-valued operators; Hausdorff-Pompeiu generalized semi-metric; contractive type set-valued operators; semicontinuous set-valued operators; uniform -continuity; set-valued operators; continuous dependence of the fixed points set},
language = {eng},
number = {1-2},
pages = {29-41},
title = {Continuous dependence on parameters of the fixed points set for some set-valued operators},
url = {http://eudml.org/doc/275885},
volume = {17},
year = {1997},
}
TY - JOUR
AU - Eduard Kirr
AU - Adrian Petruel
TI - Continuous dependence on parameters of the fixed points set for some set-valued operators
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1997
VL - 17
IS - 1-2
SP - 29
EP - 41
AB - In this paper we extend the notion of I⁰-continuity and uniform I⁰-continuity from [2] to set-valued operators. Using these properties, we prove some results on continuous dependence of the fixed points set for families of contractive type set-valued operators.
LA - eng
KW - I⁰-continuity; semi-continuous set-valued operators; Hausdorff-Pompeiu generalized semi-metric; contractive type set-valued operators; semicontinuous set-valued operators; uniform -continuity; set-valued operators; continuous dependence of the fixed points set
UR - http://eudml.org/doc/275885
ER -
References
top- [1] E. Barcz, Some fixed points theorems for multi-valued mappings, Demonstratio Math. Vol. XVI, 3 (1983), 725-743. Zbl0574.54045
- [2] I. Del Prete and C. Esposito, Elementi uniti di transformazioni funzionali e teoremi di dipendenza continua, Rend. Circ. Mat. di Palermo serie 2, 23 (1974), 187-205. Zbl0321.54027
- [3] J.Dugundji, Topology, Allyn and Bacon Inc., Boston, 1966.
- [4] E. Kirr, On continuous dependence on parameters of the fixed point set for some classes of metric operators, to appear. Zbl0904.47042
- [5] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ., Dordrecht, 1991. Zbl0731.49001
- [6] A.I. Rus, Generalized contraction, Univ. Cluj-Napoca Preprint, 3 (1983), 1-130.
- [7] R.E. Smithson, Fixed points for contractive multifunctions, Proc. A.M.S., 27 (1971), 192-194. Zbl0213.24501
- [8] R. Wegrzyk, Fixed-point theorems for multi-valued functions and their applications to functional equations, Diss. Math., 201 (1982), 1-31. Zbl0521.54034
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