Browder fixed-point theorem
Mathematical theorem From Wikipedia, the free encyclopedia
Mathematical theorem From Wikipedia, the free encyclopedia
The Browder fixed-point theorem is a refinement of the Banach fixed-point theorem for uniformly convex Banach spaces. It asserts that if is a nonempty convex closed bounded set in uniformly convex Banach space and is a mapping of into itself such that (i.e. is non-expansive), then has a fixed point.
Following the publication in 1965 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 of a non-expansive map has a unique asymptotic center, which is a fixed point of . (An asymptotic center of a sequence , if it exists, is a limit of the Chebyshev centers for truncated sequences .) A stronger property than asymptotic center is Delta-limit of Teck-Cheong Lim, which in the uniformly convex space coincides with the weak limit if the space has the Opial property.
Seamless Wikipedia browsing. On steroids.
Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.
Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.