Let a be an ideal of a local ring (R, m) and M and N two finitely generated R-modules. In this paper, we introduce the concept of generalized formal local cohomology modules. We define i-th generalized formal local cohomology module of M and N with respect to a by F₀ⁱ (M, N): = nHₘⁱ (M, N/a^nN) for i 0. We prove several results concerning vanishing and finiteness properties of these modules.
Rezaei et al. (Sun,) studied this question.