Existence for nonconvex integral inclusions via fixed points

Aurelian Cernea

Archivum Mathematicum (2003)

  • Volume: 039, Issue: 4, page 293-298
  • ISSN: 0044-8753

Abstract

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We consider a nonconvex integral inclusion and we prove a Filippov type existence theorem by using an appropiate norm on the space of selections of the multifunction and a contraction principle for set-valued maps.

How to cite

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Cernea, Aurelian. "Existence for nonconvex integral inclusions via fixed points." Archivum Mathematicum 039.4 (2003): 293-298. <http://eudml.org/doc/249127>.

@article{Cernea2003,
abstract = {We consider a nonconvex integral inclusion and we prove a Filippov type existence theorem by using an appropiate norm on the space of selections of the multifunction and a contraction principle for set-valued maps.},
author = {Cernea, Aurelian},
journal = {Archivum Mathematicum},
keywords = {integral inclusions; contractive set-valued maps; fixed point; contractive set-valued maps; Banach space; Filippov-type inequality},
language = {eng},
number = {4},
pages = {293-298},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Existence for nonconvex integral inclusions via fixed points},
url = {http://eudml.org/doc/249127},
volume = {039},
year = {2003},
}

TY - JOUR
AU - Cernea, Aurelian
TI - Existence for nonconvex integral inclusions via fixed points
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 4
SP - 293
EP - 298
AB - We consider a nonconvex integral inclusion and we prove a Filippov type existence theorem by using an appropiate norm on the space of selections of the multifunction and a contraction principle for set-valued maps.
LA - eng
KW - integral inclusions; contractive set-valued maps; fixed point; contractive set-valued maps; Banach space; Filippov-type inequality
UR - http://eudml.org/doc/249127
ER -

References

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  1. Castaing C., Valadier M., Convex Analysis and Measurable Multifunctions, LNM 580, Springer, Berlin, 1977. (1977) Zbl0346.46038MR0467310
  2. Cernea A., A Filippov type existence theorem for infinite horizon operational differential inclusions, Stud. Cerc. Mat. 50 (1998), 15–22. (1998) Zbl1026.34070MR1837385
  3. Cernea A., An existence theorem for some nonconvex hyperbolic differential inclusions, Mathematica 45(68) (2003), 101–106. Zbl1084.34508MR2056043
  4. Kannai Z., Tallos P., Stability of solution sets of differential inclusions, Acta Sci. Math. (Szeged) 63 (1995), 197–207. (1995) Zbl0851.34015MR1377359
  5. Lim T. C., On fixed point stability for set valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl. 110 (1985), 436–441. (1985) Zbl0593.47056MR0805266
  6. Petruşel A., Integral inclusions. Fixed point approaches, Comment. Math. Prace Mat., 40 (2000), 147–158. Zbl0991.47041MR1810391
  7. Tallos P., A Filippov-Gronwall type inequality in infinite dimensional space, Pure Math. Appl. 5 (1994), 355–362. (1994) MR1343457
  8. Zhu Q. J., A relaxation theorem for a Banach space integral-inclusion with delays and shifts, J. Math. Anal. Appl. 188 (1994), 1–24. (1994) Zbl0823.34023MR1301713

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