ASYMPTOTIC BEHAVIOR OF GENERALIZED SOLUTIONS IN BANACH SPACES

Let X be a real Banach space with norm vertical bar . vertical bar and let I denote the identity operator. Then an operator A.contnd.X*X with domain D(A) and range R(A) is said to be accretive if vertical bar x$_{1}$-x$_{2}$ vertical bar.leq.vertical bar x$_{1}$-x$_{2}$+r(y$_{1}$-y$_{2}$) vertical bar for all y$_{i}$.mem.Ax$_{i}$, i=1, 2, and r>0. An accretive operator A.contnd.X*X is m-accretive if R(I+rA)=X for all r>0.r>0.