On n-weak biamenability of Banach algebras

In this paper,  the notion of n-weak biamenability of Banach algebras is introduced and for every n\geq 3, it is shown that n-weak biamenability of the second dual A^{**} of a Banach algebra A implies n-weak biamenability of A and this  is true for n=1, 2 under some mild conditions.   As a concrete example,  it is  shown that for every abelian locally compact group G, L^1(G) is 1-weakly biamenable and  \ell^1(G) is n-weakly biamenable for every odd integer n.