An n-dimensional mixed-type additive and quadraticfunctional equation and its stability

摘要

We determine the general solution of the n-dimensional mixed-type additive and quadratic functionalequation, 2f (Σ_(i=1)~n x_i) +Σ_(1≤i,j≤n,i≠j)f (x_i- j)= n+1) i=1)~nf(x_+(-nf(-i),where n > 1,and investigate its general stability.