Approximation of adjoint of a multiplier on banach algebras

For a Banach algebra A, we denote by A* and A** the first and the second duals of A respectively. Let T be a mapping from A* to itself. In this article, we will investigate some stability results concerning the equationsT(αf+βg)=αT(f)+βT(g),  T(αf)=αT(f)T(αf+βg)=αT(f)+βT(g),  T(αf)=αT(f)andT(αf+βg)+T(αf−βg)=2α2T(f)+2β2T(g)T(αf+βg)+T(αf−βg)=2α2T(f)+2β2T(g)where f,g ∈ A*, a ∈ A  , and α,β∈ℚ\{0}α,β∈ℚ\{0}.