Generalized MPD and DMP Inverses
Dijana Mosić · Numerical Functional Analysis and Optimization · 2024
For a generalized Drazin invertible operator A and its core–EP inverse A◯d, the expression AA◯dA plays important role in the representations of well-known generalized inverses, in theory of partial orders and for decompositions of operator A. Solving certain system of operator equations leads to introduction of new generalized inverse of AA◯dA. Since this new inverse can be expressed by the generalized Moore–Penrose inverse and generalized Drazin inverse of A, it is called a generalized MPD inverse of AA◯dA. As a dual version of generalized MPD inverse, we also consider a generalized DMP inverse. The dual core inverse and core inverse of A, respectively, are special cases of the generalized MPD inverse and generalized DMP inverse. Several properties, representations and characterizations of generalized MPD and DMP inverses are established. Applying the generalized MPD and DMP inverses, we solve corresponding systems of linear equations and minimization problems. One well-known minimization problem is a particular case of our results.