In the 1980s, a question was raised by János Aczél, whether it is possible to solve functional equations with the help of computer programs. Since then, many researchers have used computers as assistants for their studies of functional equations and related topics. The main goal of this dissertation is to perform some studies on functional equations and their related topic – convexity, with the help of computers. More precisely, we introduce the computer packages developed in the Computer Algebra system Maple that investigate some specific functional equations and convexity problems. They enrich the field of computer algebraic investigations of functional equations and inequalities described.