A new concept of a generalized solution of operator equations in a Banach space

We define a new notion of a generalized solution of an operator equation with a closed linear operator in a Banach space as an element of the completion of this space with respect to some locally convex topology. We prove a theorem on the existence and uniqueness of the generalized solution. Bibliography: 5 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 93–99.