# uniformly convex space

(redirected from Uniformly convex Banach space)

## uniformly convex space

[¦yü·nə‚fȯrm·lē ¦kän‚veks ′spās]
(mathematics)
A normed vector space such that for any number ε > 0 there is a number δ > 0 such that, for any two vectors x and y, if │ x │ ≤ 1 + δ, │ y │ ≤ 1 + δ, and │ x + y │ > 2, then │ x-y │ < ε.="" also="" known="" as="" uniformly="" rotund="">
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Let H be a uniformly convex Banach space and the set Q be a closed, bounded, and convex subset of H.
Let E be a uniformly convex Banach space with a Frechet differentiable norm and let C be a nonempty subset of E.
 (Demiclosed principle) Let C be a nonempty closed convex subset of a uniformly convex Banach space E and S : C [right arrow] C be a nonexpansive mapping.
As an example, any locally uniformly convex Banach space (in particular, any uniformly convex Banach space) possesses the Kadec-Klee property (see Diestel [8, Chapter 2, Theorem 3 and Theorem 4(iii)]).
Using these, we present some examples, one of which is a uniformly convex Banach space which is not p-uniformly convex.
Let X be a uniformly convex Banach space; for any bounded set B of X, there exist k, l > 0 and T > 0, and a finite dimension subspace [X.sub.1] of X, such that
Let E be a uniformly convex Banach space, C be a nonempty closed convex subset of E, and S:C [right arrow] C be a nonexpansive mapping.
Let E be a uniformly convex Banach space and 0 < p [less than or equal to] [t.sub.n] [less than or equal to] q < 1 for all n [member of] N.
It is known (cf.[4, 13]) that [W.sup.1,p](G, [[omega].sub.0], [[omega].sub.1]) is a uniformly convex Banach space, provided
Recently, many authors studied a great number of iterative methods for solving a common element of the set of fixed points for a nonexpansive mapping and the set of solutions to a mixed equilibrium problem in the setting of Hilbert space and uniformly smooth and uniformly convex Banach space, respectively (please see, e.g., [1-11] and the references therein).
Let E be a uniformly convex Banach space, K be a nonempty closed convex subset of E.

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