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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

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A generalization of Anderson’s theorem on unimodal functions
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by Somesh Das Gupta PDF
Proc. Amer. Math. Soc. 60 (1976), 85-91 Request permission

Abstract:

Anderson (1955) gave a definition of a unimodal function on ${R^n}$ and obtained an inequality for integrals of a symmetric unimodal function over translates of a symmetric convex set. Anderson’s assumptions, especially the role of unimodality, are critically examined and generalizations of his inequality are obtained in different directions. It is shown that a marginal function of a unimodal function (even if it is symmetric) need not be unimodal.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 85-91
  • MSC: Primary 26A87; Secondary 52A40
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0425050-7
  • MathSciNet review: 0425050