Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



A generalization of Anderson’s theorem on unimodal functions

Author: Somesh Das Gupta
Journal: Proc. Amer. Math. Soc. 60 (1976), 85-91
MSC: Primary 26A87; Secondary 52A40
MathSciNet review: 0425050
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A87, 52A40

Retrieve articles in all journals with MSC: 26A87, 52A40

Additional Information

Keywords: Unimodal function, convex set, invariance, marginal function, inequalities
Article copyright: © Copyright 1976 American Mathematical Society