AN INEQUALITY IN THE THEORY OF NETWORKS WITH MONOTONE ELEMENTS

We consider a certain inequality that arises in the study of iterative methods for solving equations in a Hilbert space, and give equivalent characterizations of the inequality, We then show that the inequality is satisfied by the members of a large class of networks of monotone (possibly dynamic) two-terminal elements. This establishes the applica bility of a simple algorithm that, for a large class of monotone resis tive networks, will converge to a solution of the network equations wh enever a solution exists, and that will generate an unbounded sequence of iterates if no solution exists.