Extension of Simons' inequality
Authors:
Kersti Kivisoo and Eve Oja
Journal:
Proc. Amer. Math. Soc. 133 (2005), 34853496
MSC (2000):
Primary 39B62, 46A55, 46B20, 54C30
Published electronically:
June 28, 2005
MathSciNet review:
2163583
Fulltext PDF Free Access
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Abstract: We prove the following extended version of Simons' inequality and present its applications. Let be a set and be a subset of . Let be a subset of a Hausdorff topological vector space which is invariant under infinite convex combinations. Let be a bounded function such that the functions are convex for all and whenever , and Let be a sequence in . Assume that, for every , there exists satisfying . Then
If , then the set in the above inequality can be replaced by .
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Some applications of Simons' inequality, Serdica Math. J. 26 (2000), 5978. MR 1767034 (2002c:46026)
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 G. GODEFROY, V. ZIZLER,
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Additional Information
Kersti Kivisoo
Affiliation:
Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, EE50409 Tartu, Estonia
Email:
kersti.kivisoo@mail.ee
Eve Oja
Affiliation:
Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, EE50409 Tartu, Estonia
Email:
eveoja@math.ut.ee
DOI:
http://dx.doi.org/10.1090/S0002993905082675
PII:
S 00029939(05)082675
Keywords:
Simons' inequality,
convex sets in topological vector spaces,
convex functions,
uniformly convergent convex combinations,
Banach space geometry.
Received by editor(s):
July 2, 2004
Published electronically:
June 28, 2005
Additional Notes:
This research was partially supported by Estonian Science Foundation Grant 5704
Communicated by:
Jonathan M. Borwein
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
