Higher Derivations Associated with the Cauchy-Jensen Type Mapping

Let H be an infinite–dimensional Hilbert space and K(H) be the set of all compact operators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher Jordan derivation on K(H) associated with the following Cauchy–Jencen type functional equation 2f( T + S 2 + R) = f(T) + f(S) + 2f(R) for all T, S, R ∈ K(H).