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<blockquote>'''Tikhonov (Tychonoff) fixed point theorem:''' Let ''V'' be a [[locally convex topological vector space]], for any non-empty compact convex set ''X'' in ''V'', any continuous function ''f'' : ''X'' → ''X'' has a fixed point.</blockquote>
<blockquote>'''Browder fixed point theorem:''' Let ''K'' be a nonempty closed bounded convex set in a [[uniformly convex Banach space]], then any non-expansive function ''f'' : ''K'' → ''K'', has a fixed point. (A function <math>f</math> is called non-expansive if <math>\|f(x)-f(y)\|\leq \|x-y\| </math> for each <math>x</math> and <math>y</math>.)</blockquote>
Other results include the [[Markov–Kakutani fixed-point theorem]] (1936-1938) and the [[Ryll-Nardzewski fixed-point theorem]] (1967) for continuous affine self-mappings of compact convex sets, as well as the [[Earle–Hamilton fixed-point theorem]] (1968) for holomorphic self-mappings of open domains.
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