uniformly convex space


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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 B be a uniformly convex space. Then for every d > 0, [epsilon] > 0, and for arbitrary vectors, [x.sub.1], [x.sub.2] [member of] B with [parallel][x.sub.1][parallel] [less than or equal to] d, [parallel][x.sub.2][parallel] [less than or equal to] d, and [parallel][x.sub.1]-[x.sub.2][parallel]/C [greater than or equal to] [epsilon], where C [greater than or equal to] 1, there exists [delta] > 0 such that
Let B be a uniformly convex space and [alpha] [member of] (0, 1).
Salame, Nonlinear common fixed point properties for semi-topological semigroups in uniformly convex spaces (Accepted, Journal of Fixed Point Theory and Applications).

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