Solution of the Second Order Cauchy Difference Equation On Free Monoid

Abstract

Let h:S → T be a function, where (S,.)is a monoid and (T,+) is an abelian group. In this paper, the following Second Order Cauchy difference of h : C(2)h(p1,p2,p3) = h(p1p2p3)−h(p1p2)−h(p1p3)−h(p2p3)+ h(p1)+h(p2)+h(p3)∀p1,p2,p3∈S is studied. We give some special solutions of C(2)h=0 on free Monoid.