Some remark on the functional equation

Abstract

The appearance of function equations can be traced back to a long time ago. The oldest and perhaps the best-known function equation is the Cauchy function equation.

The trivial solution of Cauchy equation is simple, but the general solution is very complex.

Later several function equations appeared, which either arose during some practical problem or became known from a theoretical perspective. The function equation Hosszú is also such a function equation, introduced by Miklós Hosszú based on theoretical considerations. We further generalize the Hosszú-type functional equation and give its solution.