Skip to main content
    • Aa
    • Aa

On nearly uniformly convex Banach spaces

  • J. R. Partington (a1)

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.

Linked references
Hide All

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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *