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The Browder fixed-point theorem is a refinement of the Banach fixed-point theorem for uniformly convex Banach spaces. It asserts that if K {\displaystyle K} is a nonempty convex closed bounded set in uniformly convex Banach space and f {\displaystyle f} is a mapping of K {\displaystyle K} into itself such that ‖ f − f ‖ ≤ ‖ x − y ‖ {\displaystyle \|f-f\|\leq \|x-y\|} , then f {\displaystyle f} has a fixed point.
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