CONTINUOUS Solutions of Cauchy's POWER functional equation

Cauchy's power functional equation is the last of the four functional equations that Cauchy introduced and became the cornerstone of the area of functional equations. This video presents its solution when the function which satisfies the equation is assumed to be continuous. Four different solutions are given. Three of them assume known the solutions of the previous three functional equations. Then, using a transformation of variables the fourth equation is reduced to one of the previous equations. The fourth solution uses the ZQR method. (The method is thus named by mathematician Costas Efthimiou since it computes the values of the function successively for Z, Q, and R.) The method computes the solutions from scratch without relying on any other functional equation.