Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A class of absolute retracts in spaces of integrable functions


Authors: Alberto Bressan, Arrigo Cellina and Andrzej Fryszkowski
Journal: Proc. Amer. Math. Soc. 112 (1991), 413-418
MSC: Primary 47H15; Secondary 34A60, 47H10, 49J24, 54C15
MathSciNet review: 1045587
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a class of subsets of $ {L^1}$, that are shown to be absolute retracts, that contains at once decomposable sets and sets of solutions to Lipschitzean differential inclusions. In this way we generalize and unify a number of different previous results.


References [Enhancements On Off] (What's this?)

  • [1] Jean-Pierre Aubin and Arrigo Cellina, Differential inclusions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 264, Springer-Verlag, Berlin, 1984. Set-valued maps and viability theory. MR 755330
  • [2] Alberto Bressan and Giovanni Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), no. 1, 69–86. MR 947921
  • [3] Arrigo Cellina, On the set of solutions to Lipschitzian differential inclusions, Differential Integral Equations 1 (1988), no. 4, 495–500. MR 945823
  • [4] Arrigo Cellina and António Ornelas, Representation of the attainable set for Lipschitzian differential inclusions, Rocky Mountain J. Math. 22 (1992), no. 1, 117–124. MR 1159946, 10.1216/rmjm/1181072798
  • [5] R. M. Colombo, A. Fryszkowski, T. Rzezukowski, and V. Staicu, Continuous selections of solutions sets of Lipschitzean differential inclusions, Funk. Ekv. (to appear).
  • [6] Andrzej Fryszkowski, Continuous selections for a class of nonconvex multivalued maps, Studia Math. 76 (1983), no. 2, 163–174. MR 730018
  • [7] Fumio Hiai and Hisaharu Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, J. Multivariate Anal. 7 (1977), no. 1, 149–182. MR 0507504
  • [8] A. Ornelas, A continuous version of the Filippov-Gronwall inequality for differential inclusions, Rend. Sem. Mat. Univ. Padova (to appear).
  • [9] B. Ricceri, Une proprieté topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes, preprint.
  • [10] Kôsaku Yosida, Functional analysis, 6th ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin-New York, 1980. MR 617913

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H15, 34A60, 47H10, 49J24, 54C15

Retrieve articles in all journals with MSC: 47H15, 34A60, 47H10, 49J24, 54C15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1045587-8
Article copyright: © Copyright 1991 American Mathematical Society