Proper Splitting for the Generalized Inverse ${A}_{T,S}^{(2)}$ and Its Application on Banach Spaces

A possible type of the operator splitting is studied. Using this operator splitting, we introduce some properties and representations of generalized inverses as well as iterative method for computing various solutions of the restricted linear operator system $Ax=b, x\in T$ , where $A\in {\scr L}(\textbf{X},\textbf{Y})$ and T is an arbitrary but fixed subspace of X.