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<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. Also, Aniki & Rauf (2019) presented some interesting results on the stability of partially ordered metric spaces for coupled fixed point iteration procedures for mixed monotone mappings.
<blockquote>'''[[Kakutani fixed-point theorem]]:''' Every correspondence that maps a compact convex subset of a locally convex space into itself with a closed graph and convex nonempty images has a fixed point.</blockquote>
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* Andrzej Granas and [[James Dugundji]], ''Fixed Point Theory'' (2003) Springer-Verlag, New York, {{isbn|0-387-00173-5}}.
* William A. Kirk and [[Brailey Sims]], ''Handbook of Metric Fixed Point Theory'' (2001), Kluwer Academic, London {{isbn|0-7923-7073-2}}.
* Samuel A. Aniki and Kamilu Rauf, ''Some stability results in partially ordered metric spaces for coupled fixed point iteration of procedures for mixed monotone mappings'' (2019), Islamic University Multidisciplinary Journal, 6(3), 175-186
==External links==
*
[[Category:Fixed-point theorems]]
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