- Title
- Uniformly convex functions on Banach Spaces
- Creator
- Borwein, Jonathan M.; Guirao, A. J.; Hájek, P.; Vanderwerff, J.
- Relation
- Proceedings of the American Mathematical Society Vol. 137, Issue 3, p. 1081-1091
- Publisher Link
- http://dx.doi.org/10.1090/S0002-9939-08-09630-5
- Publisher
- American Mathematical Society
- Resource Type
- journal article
- Date
- 2009
- Description
- Given a Banach space (Χ,∥ · ∥), we study the connection between uniformly convex functions f : Χ → R bounded above by ∥ · ∥ᵖ and the existence of norms on X with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function f : Χ → ℝ bounded above by ∥ · ∥² if and only if Χ admits an equivalent norm with modulus of convexity of power type 2.
- Subject
- convex function; uniformly smooth; uniformly convex; superreflexive
- Identifier
- http://hdl.handle.net/1959.13/807956
- Identifier
- uon:7553
- Identifier
- ISSN:0002-9939
- Rights
- First published in the Proceedings of the American Mathematical Society in 2009, published by the American Mathematical Society.
- Language
- eng
- Full Text
- Reviewed
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