A fixed-point theorem is a fundamental result in various branches of mathematics, particularly in analysis and topology, that asserts the existence of fixed points under certain conditions. A fixed point of a function is a point that is mapped to itself by the function. Formally, if \( f: X \rightarrow X \) is a function on a set \( X \), then a point \( x \in X \) is a fixed point if \( f(x) = x \).
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