The relations between '-amenability and some special ideals

In this paper we determine '-amenability of a Banach algebraA with some certain ideals in its second dual A00. We show that foran idempotent m 2 A00, the set C m = f m : 2 Cg is a leftideal in A00 if and only if m is a '-mean. We also give some resultson the relationships between weak amenability and '-amenability ofBanach algebras

Higher *-derivations between unital C*-algebras

Let A, B be two unital C*-algebras. We prove that every sequence of mappings from A into B, H = {h0,h1, ..., hm, ...}, which satisfy hm(3nuy) =Σi+j=mhi(3nu)hj(y) for each m ∈ N0, for all u∈U(A), all y∈ A, and all n = 0, 1, 2, ..., is a higher derivation. Also, for a unital C*-algebra A of real rank zero, every sequence of continuous mappings from A into B, H = {h0,h1,..., hm, ...}, is a higher derivation when hm(3nuy)=Σi+j=mhi(3nu)hj(y) holds for all u∈I1(Asa), all y∈ A, all n = 0, 1,2, ... and for each m ∈ N0. Furthermore, by using the fixed points methods, we investigate the Hyers-Ulam-Rassias stability of higher *-derivations between unital C*-algebras