Functional equations are mathematical equations where the unknowns are functions rather than simple variables. These equations often express a relationship between the values of a function at different points. Solving functional equations typically involves finding a function that satisfies the given conditions, which can be a challenging task. Common examples of functional equations include the Cauchy functional equation and the Additive Cauchy equation. These equations have applications in various fields, including analysis, number theory, and mathematical physics. Understanding functional equations can provide insights into the behavior of functions and their properties.