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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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Mean value inequalities in Hilbert space
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by F. H. Clarke and Yu. S. Ledyaev PDF
Trans. Amer. Math. Soc. 344 (1994), 307-324 Request permission


We establish a new mean value theorem applicable to lower semi-continuous functions on Hilbert space. A novel feature of the result is its "multidirectionality": it compares the value of a function at a point to its values on a set. We then discuss some refinements and consequences of the theorem, including applications to calculus, flow invariance, and generalized solutions to partial differential equations. Résumé. On établit un nouveau théorème de la valeur moyenne qui s’applique aux fonctions semicontinues inférieurement sur un espace de Hilbert. On déduit plusieurs conséquences du résultat portant, par exemple, sur les fonctions monotones et sur les solutions généralisées des équations aux dérivées partielles.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 344 (1994), 307-324
  • MSC: Primary 49J52; Secondary 26A24, 47H99, 47N10, 49L25
  • DOI:
  • MathSciNet review: 1227093