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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Densely defined selections of multivalued mappings
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by M. M. Čoban, P. S. Kenderov and J. P. Revalski PDF
Trans. Amer. Math. Soc. 344 (1994), 533-552 Request permission

Abstract:

Rather general suficient conditions are found for a given multivalued mapping $F:X \to Y$ to possess an upper semicontinuous and compact-valued selection G which is defined on a dense ${G_\delta }$-subset of the domain of F. The case when the selection G is single-valued (and continuous) is also investigated. The results are applied to prove some known as well as new results concerning generic differentiability of convex functions, Lavrentieff type theorem, generic well-posedness of optimization problems and generic non-multivaluedness of metric projections and antiprojections.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 344 (1994), 533-552
  • MSC: Primary 54C65; Secondary 46G99, 47H04, 49J40, 54C60
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1154539-6
  • MathSciNet review: 1154539