GENERALIZED HYERS–ULAM STABILITY OF A FUNCTIONAL EQUATION OF HOSSZU ́ TYPE

Abstract

The aim of the present paper is to give general solutions of the following functional equation of Hosszú type:

f(x − y + xy) + f(y) = f(x) + f(xy)

and its Pexiderized version

f(x − y + xy) + g(y) = h(x) + k(xy),

and prove the Hyers-Ulam stability of the above two functional equations in Banach spaces.