Some remarks on Cauchy equation on a curve

Abstract

In recent years a still increasing number of papers have been dealing with so called conditional Cauchy equations. The problem can be briefly stated as follows. Let X and E be some nonempty sets and let o :XxX-—X and* :ExE —»-E be some binary operations. Further, let Z c X * X be a nonempty set. Consider the following functional equation for f : X — E (usually called Cauchy functional equation) (Fragment tekstu).