On the General and Measurable Solutions of some Functional Equations

Abstract

The general solutions of two functional equations, without imposing any regularity condition on any of the functions appearing, have been obtained. From these general solutions, the Lebesgue measurable solutions have been deduced by assuming the function(s) to be measurable in the Lebesgue sense.

Keywords

• logarithmic function
• multiplicative function
• function measurable in the Lebesgue sense
• continuous function
• stability of a functional equation
• the Shannon entropy