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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
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Book and Papers for properties of uniformly convex and locally uniformly convex and strictly...
I would recommend you a nice book by B. Beauzamy titled "Introduction to Banach spaces and their geometry". See also this article
http://www.ams.org/journals/tran/1955-078-01/S0002-9947-1955-0066558 …