The Method of Lines and the Approximation of Zeros of m-Accretive Operators in General Banach Spaces

It is shown that a zero of an m-accretive operator T: D(T) X → 2X, in a general Banach space X, can be approximated via methods of lines for associated evolution equations. Results of Browder for (single-valued) locally defined continuous accretive operators T in spaces X with uniformly convex duals, or uniformly continuous accretive operators T in general Banach spaces X, are extended to the present case. Results of Reich for m-accretive operators in reflexive Banach spaces are also extended to the present setting. Unlike Browder′s results, our estimates do not use the modulus of continuity of the operators T or the duality mapping of X. Kobayashi-type estimates are used for the bounds involving the normed differences between the endpoints of the methods of lines and a zero of T.