ON THE CAUCHY EQUATION ON SPHERES

Abstract

We deal with a conditional functional equationϕ(x) = ϕ(y)  implies  f(x+y) = f(x)+f(y).Under some assumptions imposed on function ϕ, the domains and ranges of ϕ and f we derive the additivity of f. As a consequence we obtain two Hyers-Ulam stability results related to the equation considered.