Real Analysis in Functional Equations

In this article, we will showcase some analytical concepts that can be used to tackle Functional Equations (FE) in the positive real numbers domain. Such concepts and related techniques have occasionally appeared in recent High School Math Olympiads, and they are often accompanied neatly by other known techniques. In each section, we develop a theoretical background; next, we briefly mention methods that employ the theory and conclude the article by providing unsolved problems that the reader can try independently.