Lipschitz Continuity

Lipschitz continuity is a property of a function that guarantees it doesn't change too rapidly. Specifically, there exists a constant—called the Lipschitz constant—that bounds how much the function's output can differ when its input changes. In practical terms, if you move a small amount in the input, the change in the output is limited and predictable. This concept ensures the function’s graph doesn’t have any steep spikes or sudden jumps, making it stable and well-behaved. It’s a useful way to measure and control how smoothly a function varies across its domain.