  We present new additive results for the group inverse in a Banach algebra
under certain perturbations. The upper bound of $\|(a+b)^{\#}-a^d\|$ is thereby
given. These extend the main results in [X. Liu, Y. Qin and H. Wei,
Perturbation bound of the group inverse and the generalized Schur complement in
Banach algebra, Abstr. Appl. Anal., 2012, 22 pages. DOI:10.1155/2012/629178].
