W-weighted GDMP inverse for rectangular matrices

In this article, we introduce two new generalized inverses for rectangular matrices called $W$-weighted generalized-Drazin--Moore--Penrose (GDMP) and generalized-Drazin-reflexive (GDR) inverses. The first inverse can be seen as a generalization of the recently introduced GDMP square matrix to matrix. second class contains inverse. We then exploit their various properties establish that proposed coincide with different well-known under certain assumptions. also obtain representation employing EP-core nilpotent decomposition. define dual analogue results. Further, discuss additive properties, reverse- forward-order laws GD, GDMP,