PERMUTING TRIDERIVATIONS AND PERMUTING TRIHOMOMORPHISMS IN BANACH ALGEBRAS

Abstract

Using the direct method, we prove the Hyers-Ulam stability of permuting triderivations and permuting trihomomorphisms in Banach algebras and unital C*-algebras associated with the triadditive s functional inequality

parallel to f(x + y, z - w, a + b) + f (x - y, z + w, a - b) - 2f(x, z, a)+2f(x, w, b) -2 f (y, z, b) + 2f (y, w, a)parallel to <=parallel to s(2f ((x + y)/2, z - w , a + b) + 2 f ((x - y)/2, z + w, a - b) - 2f (x, z, a) + 2f (x, w, b) - 2f (y, z, b) + 2 f (y, w, d))parallel to,

where s is a fixed nonzero complex number with vertical bar s vertical bar < 1.