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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Continuity of maximal monotone sets in Banach space
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by R. E. Showalter
Proc. Amer. Math. Soc. 42 (1974), 543-546
DOI: https://doi.org/10.1090/S0002-9939-1974-0333850-5

Abstract:

A monotone set-valued map of a Banach space to its dual is shown to map line segments into bounded sets. It follows that convergent sequences are mapped into bounded sets and, when the space is separable or reflexive, this imposes continuity requirements on maximal monotone maps.
References
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 42 (1974), 543-546
  • MSC: Primary 47H05
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0333850-5
  • MathSciNet review: 0333850