In this paper we consider the Darboux type properties for the paratingent. We review some of the standard facts on the multivalued functions and the paratingent. We prove that the paratingent has always the Darboux property but the property D* holds only when the paratingent is a multivalued function.
@article{bwmeta1.element.doi-10_2478_v10062-008-0008-0,
author = {Ma\l gorzata Fedor and Joanna Szyszkowska},
title = {Darboux type properties of the paratingent},
journal = {Annales UMCS, Mathematica},
volume = {62},
year = {2008},
pages = {67-74},
zbl = {1183.26036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-008-0008-0}
}
Małgorzata Fedor; Joanna Szyszkowska. Darboux type properties of the paratingent. Annales UMCS, Mathematica, Tome 62 (2008) pp. 67-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-008-0008-0/
Czarnowska, J., Kwiecińska, G., On the Darboux property of mulivalued functions, Demonstratio Math. 25 (1992), 193-199. | Zbl 0765.54010
Delahaye, J. P., Denel, J., The continuites of the point-to-set maps, definitions and equivalences, Math. Programming Stud. 10 (1979), 8-12.
Hu, S., Papageorgiou, N. S., Handbook of Multivalued Analysis. Vol. I. Theory, Kluwer Academic Publisher, Dordrecht, 1997. | Zbl 0887.47001
Rudin, W., Principles of Mathematical Analysis, Third edition, McGraw-Hill Book Co., New York-Auckland-Düsseldorf, 1976. | Zbl 0346.26002
Zygmunt, W., On the full solution of the paratingent equations, Ann. Univ. Mariae Curie-Skłodowska Sect. A 26 (1972), 103-108 (1974).