a restriot domain D being some subset of ft" are stable. Moreover, we shall use a suoh type result to give a positive answer to a problem of K. Nikodem ([3], [4]). Let (X, ||*||) be a real Banach space and let D be a subset of X. We say that a function fiD--X is ¿-additive (t3>0 is fixed) in D iff for all x,yeD suoh that x+y e D. Similarly, we say that fiD-X is 6-Jensen function iff (2) ||2ft^) -f(x) -f(y)||^£ for all x,y e D suoh that If D -R* and (1) holds true with C « 0 we say that f is

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... tive funotion and every funotion fsD--X satisfying (2) with £ -0 is oalled Jensen funotion. P. Skof in [5] has proved that if f 1 [o,a)--X, a>0, is e -additive then there exists an additive funotion Ft R--X suoh that ||f(x) -F(x)||^ 3e for each x e [0,a).