Ali Ghaffari - Department of Mathematics, Semnan University, P.O.Box ۳۵۱۹۵-۳۶۳, Semnan, Iran.
Samaneh Javadi - Department of Mathematics, Semnan University, P.O.Box ۳۵۱۹۵-۳۶۳, Semnan, Iran.

We introduce the notions of \mathcal{T}_{M}-amenability and \phi-\mathcal{T}_{M}-amenability. Then, we characterize \phi-\mathcal{T}_{M}-amenability  in terms of WAP-diagonals and \phi-invariant means. Some concrete cases are also discussed.

Amenability, Banach algebras, derivation, group algebra, invariant mean