  Motivated by the very recent work of Gao, Y., Chen, J., Wang, J., Zou, H.
[Comm. Algebra, 49(8) (2021) 3241-3254; MR4283143], we introduce two new
generalized inverses named weak Drazin (WD) and weak Drazin Moore-Penrose
(WDMP) inverses for elements in rings. A few of their properties are then
provided, and the fact that the proposed generalized inverses coincide with
different well-known generalized inverses under certain assumptions is
established. Further, we discuss additive properties, reverse-order law and
forward-order law for WD and WDMP generalized inverses. Some examples are also
provided in support of the theoretical results.
