The method of successive approximations is often applied to proving existence of solutions to various classes of functional equations; moreover, the proof of convergence of these approximations leans on the fact that the equation under study may be majorised by another equation of a simple kind. Similar proofs may be encountered in the theory of infinitely many simultaneous linear equations and in the theory of integral and differential equations. Consideration ofjkbni semiordered spaces and operations between them enables us to easily develop a complete theory of such functional equations in abstract form.

"On one class of functional equations" (1936), as cited in: O'Connor, John J.; Robertson, Edmund F., "Leonid Kantorovich", MacTutor History of Mathematics archive, University of St Andrews