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The '''Browder fixed point theorem''' is a refinement of the [[Banach fixed point theorem]] for [[Uniformly convex space|uniformly convex Banach spaces]]. It asserts that if <math>K</math> is a nonempty [[convex set|convex]] closed bounded set in uniformly convex Banach space and <math>f</math> is a mapping of <math>K</math> into itself such that <math>\|f(x)-f(y)\|<=\|x-y\|</math> (i.e. <math>f</math> is ''non-expansive''), then <math>f</math> has a [[fixed point (mathematics)|fixed point]].
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