Abstract
To solve some systems of operator equations, we generalize the concepts of the W–weighted core–EP inverse, the W-gMP inverse, the generalized core–EP inverse and their duals and we define new kinds of generalized inverses which are called the weighted generalized core–EP inverse and its dual. Thus, these new inverses present wider classes of generalized inverses. We establish a number of characterizations and representations of the weighted generalized core–EP inverse and its dual. As applications of our new inverses, we solve several systems of linear equations and a minimization problem.
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