STABILITY OF SOME FUNCTIONAL EQUATIONS ON BOUNDED DOMAINS

Abstract

In this paper, we investigate the Hyers-Ulam stability of the functional equations

f(x + y ) + f(x - y) = 2f(x),

f(x + y ) + f(x - y) = 2f(x) + f(y) + f(-y),

f(px + (1-p)y) + f((1 - p)x +py)= f(x) _ f(y)

for p = 1/3 and p = 1/4, where f is a mapping from a bounded subset of R-N >= 1 into a Banach space E.