We investigate additive results for (p,q)-outer generalized inverse of elements in Banach algebra, along with the representation of this inverse in a block matrix in the Banachiewicz-Schur form. Also, we give the representation of image-kernel (p,q)-outer generalized inverse of block matrices in rings.
Additionally, we investigate the spectral properties of block matrices in a Banach algebra related to (p,q)-outer generalized inverse.