Nonlinear monotone operators and convex sets in Banach spaces
Felix E. Browder · Bulletin of the American Mathematical Society · 1965
Introduction.Let X be a real Banach space, X* its conjugate space, (w, u) the pairing between w in X* and u in X.for all w and v in C. It is the object of the present note to prove the following theorem:THEOREM 1.Let C be a closed convex subset of the reflexive Banach space X with 0£C, Ta monotone mapping of Cinto X*.Suppose that T is continuous from line segments in C to the weak topology of X* while