Kannan's Fixed-Point Theorem

Kannan's Fixed-Point Theorem states that in a complete metric space, if a function consistently pulls points closer together by a certain proportion, then there is exactly one point where applying the function leaves it unchanged—this is the fixed point. Imagine a process where each step brings you nearer to a specific point, and over time, you converge to that unique, stable position. This theorem guarantees both the existence and uniqueness of such a point, providing a foundation for solving complex equations and ensuring that iterative methods will converge to a single solution under the right conditions.