STABILITY AND SUPERSTABILITY OF (f(r), f(8))-DOUBLE DERIVATIONS IN QUASI-BANACH ALGEBRAS

Abstract

In this paper, the following functional equation Sigma(n)(k=2)[Sigma(k)(i1=2)Sigma(k+1)(i2=i1+1) center dot center dot center dot Sigma(n)(in-k+1=in-k+1) f( Sigma(n)i=1,i not equal(1),...,i(n-k+1) a(i)x(i) - Sigma(n-k+1) (r=1) a(ir)x(ir) - Sigma(n-k+1)(r=1))] +f(Sigma(n)(i=1)) = a(1)center dot 2(n-1) f(x(1)) is considered (n ˃= 2), and the Hyers-Ulam stability and superstability of (f(r), f(8))-double derivations on quasi-Banach algebras associated with the functional equation (0.1) are proved.