SUPERSTABILITY AND STABILITY OF (r, s, t)-J*-HOMOMORPHISMS: FIXED POINT AND DIRECT METHODS

Abstract

In this paper, we introduce the following useful functional equations:

f(x + y) f(x - 2y) + f (y - x) = f(x), (0.1)

f(Sigma(p)(i=1) x(i)/p - 1) + Sigma(p)(i=2) f (Sigma(p)(j=1j not equal 1) x(j) - px(i)/p - 1) + f(Sigma(p)(i=2) x(i)-x(1)/p - 1) = f(x(1)) (0.2)

and prove the superstability and the Hyers-Ulam stability of (r,s,t)-J*-homomorphisms, associated with those, by using the fixed point method and the direct method.