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==History==
Following the publication in 1995 of two independent versions of the theorem by Felix Browder and by William Kirk, a new proof of Michael Edelstein showed that, in a uniformly convex Banach space, every iterative sequence <math>f^nx_0</math> of a non-expansive map <math>f</math> has a unique asymptotic center, which is a fixed point of <math>f</math>. (An ''asymptotic center'' of a sequence <math>(x_k)_{k\in\mathbb N}</math>, if it exists, is a limit of the [[Chebyshev center]]s <math>c_n</math> for truncated sequences <math>(x_k)_{k\ge n}</math>.) A stronger property than asymptotic center is [[Delta-convergence|Delta-limit]] of T.C. Lim, which in the uniformly convex space coincides with the weak limit if the space has the [[Opial property]].
==See also==
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==References==
* F. E. Browder, Nonexpansive nonlinear operators in a Banach space. Proc.
* W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly '''72''' (1965) 1004–1006.
* M. Edelstein, The construction of an asymptotic center with a fixed-point property, Bull. Amer. Math. Soc. '''78''' (1972), 206-208.
{{Functional Analysis}}
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