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On nearly uniformly convex Banach spaces

Published online by Cambridge University Press:  24 October 2008

J. R. Partington
J. R. Partington
Affiliation:
Pembroke College, Cambridge
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Extract

A real Banach space (X, ‖ · ‖) is said to be uniformly convex (UC) (or uniformly rotund) if for all ∈ > 0 there is a δ > 0 such that if ‖x| ≤ 1, ‖y‖ ≤ 1 and ‖x−y‖ ≥ ∈, then ‖(x + y)/2‖ ≤ 1− δ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 1 , January 1983 , pp. 127 - 129
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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