Lipschitz Continuity is a mathematical concept that describes how a function behaves in relation to changes in its input. A function f is said to be Lipschitz continuous if there exists a constant L such that for any two points x_1 and x_2 , the difference in their outputs is bounded by L times the difference in their inputs. In simpler terms, this means that the function does not change too rapidly. This property is useful in various fields, including analysis and optimization, as it ensures that small changes in input lead to controlled changes in output. Lipschitz continuity helps in proving the existence and uniqueness of solutions to differential equations and is often used in numerical methods to guarantee stability and convergence.