Solvability of Equations Involving A-Proper and Pseudo-A-Proper Mappings

Let X, Y be Banach spaces with their respective duals denoted by X* and Y*, D a subset of X, T: D ⊆ X → Y a possibly nonlinear mapping, Γ = {X_n,V_n ;E_n,W_n } an approximation scheme for the equation (1.1) T ( x ) = f ( x ∈ D , f ∈ Y ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137735/46b2ebee-a99f-4a7d-b17e-b7dad9c42178/content/eq1.tif"/>