Nonlinear Accretive Operators in Banach Spaces by Felix E. Browder

for each * in X. For any Banach space X and any element * of Xt J(x) is a nonempty closed convex subset of the sphere of radius ||x|| about zero in X*. If X* is strictly convex, J is a singlevalued mapping of X into X* and is continuous from the strong topology of X to the weak* topology of X*. J is continuous in the strong topologies if and only if the norm in X is C on the complement of the origin. DEFINITION. If T is a (possibly) nonlinear mapping with domain D(T) in X and with range R(T) in X, then T is said to be accretive if for each pair x and y in D(T),