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A funtion f whose domain and range are real is Lipschitz continuous if there exists a constant M such that for all x and y, |f(x) - f(y)| <= M * |x - y|. The geometric interpretation is that if you put a cone (of constant angle) around each point of the graph of the function, the function stays inside that cone. |
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A function f whose domain and range are real is Lipschitz continuous if there exists a constant M > 0 such that |f(x) - f(y)| <= M.|x - y| for all x and y. |
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