# 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="">
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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.
4]) Let E be a uniformly convex Banach space and C be a nonempty closed bounded convex subset of E.
Let X be a uniformly convex Banach space and let Q be a nonexpansive mapping of X into X (i.
Let E be a uniformly convex Banach space, K be a nonempty closed convex subset of E.
T] is also reflexive and uniformly convex Banach space.
Groetsch [9] generalized the results of [2, 8, 10, 12, 14] in a uniformly convex Banach space by employing (1.
It is our purpose in this paper to establish some convergence results for nonexpansive and quasi-nonexpansive operators in a uniformly convex Banach space via the newly introduced iterative processes defined in (2.
Let E be a convex subset of a uniformly convex Banach space X and [T.
Let Ebea uniformly convex Banach space and let C be a nonempty closed bounded convex subset of E.
Let E be a uniformly convex Banach space and let C be a nonempty closed bounded and convex subset of E.
7) to obtain some convergence results for Mann and Ishikawa iteration processes in a uniformly convex Banach space, while Berinde [4] extended the results of [32, 33] to an arbitrary Banach space for the same iteration processes.
However, they remarked that their results are true for uniformly smooth and uniformly convex Banach spaces (see [34], p.

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