On generalizations of the Pompeiu functional equation

Abstract

ABSTRACT. In this paper, we determine the general solution of the functional equations y(=:++,)=p()+q()+()h(), (V. e .) and f(ax + by + cxy) f(x) + f(y) "4-f(x)f(y), (V x, y 6 . which are generalizations of a functional equation studied by Pompeiu. We present a method which is simple and direct to determine the general solutions of the above equations without any regularity assumptions.

On the stability of a mixed type functional equation in generalized functions

“…For this reason, equation (1.1) is called the mixed type quadratic and additive functional equation. We refer to [9][10][11][12][13][14] for the stability results of other mixed type functional equations.…”