Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A class of absolute retracts in spaces of integrable functions
HTML articles powered by AMS MathViewer

by Alberto Bressan, Arrigo Cellina and Andrzej Fryszkowski PDF
Proc. Amer. Math. Soc. 112 (1991), 413-418 Request permission

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
  • 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, DOI 10.1007/978-3-642-69512-4
  • Alberto Bressan and Giovanni Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), no. 1, 69–86. MR 947921, DOI 10.4064/sm-90-1-69-86
  • Arrigo Cellina, On the set of solutions to Lipschitzian differential inclusions, Differential Integral Equations 1 (1988), no. 4, 495–500. MR 945823
  • 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, DOI 10.1216/rmjm/1181072798
    • R. M. Colombo, A. Fryszkowski, T. Rzezukowski, and V. Staicu, Continuous selections of solutions sets of Lipschitzean differential inclusions, Funk. Ekv. (to appear).
  • Andrzej Fryszkowski, Continuous selections for a class of nonconvex multivalued maps, Studia Math. 76 (1983), no. 2, 163–174. MR 730018, DOI 10.4064/sm-76-2-163-174
  • Fumio Hiai and Hisaharu Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, J. Multivariate Anal. 7 (1977), no. 1, 149–182. MR 507504, DOI 10.1016/0047-259X(77)90037-9
    • A. Ornelas, A continuous version of the Filippov-Gronwall inequality for differential inclusions, Rend. Sem. Mat. Univ. Padova (to appear). B. Ricceri, Une proprieté topologique de l’ensemble des points fixes d’une contraction multivoque à valeurs convexes, preprint.
  • 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
Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 413-418
  • MSC: Primary 47H15; Secondary 34A60, 47H10, 49J24, 54C15
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1045587-8
  • MathSciNet review: 1045587