DECOMPOSITION OF FUNCTIONAL EQUATIONS WITH APPLICATIONS

摘要

In this paper the Decomposition Theorem for functional equations is shown. As an application of this Theorem the two times continuously differentiable solution of the functional equation G1(x(x+y)) +F1(y) = G2(y(x+y)) +F2(y) can be given with unknown functions Gi, Fi : R+ -> R (i = 1, 2) where the Equation is fulfilled for all x,y E R+ (where R+ := {x ERx> 0}).