On the asymptotic behaviour of graded generalized local cohomology modules

Let ${R=igoplus_{ngeq 0}R_n}$ be a graded Noetherian ring withlocal base ring $R_0$ and let ${R_{+}=igoplus_{ngeq 1}R_n}$.Let $M$ and $N$ be finitely generated graded $R$-modules. In thispaper, we prove some results on the asymptotic behaviour of the$n$-th graded components $H^i_{R_+}(M,N)_{n}$ of $H^i_{R_+}(M,N)$for $n o-infty$. We also study the tameness and asymptoticalstability of the homogeneous components of $H_{R_{+}}^{i}(M, N)$for some $i^{,}s$ with a specified property.