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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 93, Issue 1
  • January 1983, pp. 127-129

On nearly uniformly convex Banach spaces

  • J. R. Partington (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100060394
  • Published online: 24 October 2008
Abstract

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

(2)A. Brunel and L. Sucheston On B-convex Banach spaces. Math. Systems Theory 7 (1974), 294299.

(3)M. M. Day Some more uniformly convex spaces. Bull. Amer. Math. Soc. 47 (1941), 504507.

(5)R. Huff Banach spaces which are nearly uniformly convex. Rocky Mountain J. Maths. 10 (1980), 743749.

(6)E. Leonard Banach sequence spaces. J. Math. Anal. Appl. 54 (1976), 245265.

(7)E. J. McShane Linear functionals on certain Banach spaces. Proc. Amer. Math. Soc. 1 (1950), 402408.

(10)M. A. Smith and B. Turett Rotundity inLebesgue-Bochner function spaces. Trans. Amer. Math. Soc. 257 (1980), 105118.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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