Approximating Zeros of Accretive Operators

Let be an -accretive set in a reflexive Banach space with a Gateaux differentiable norm. For positive let denote the resolvent of . If the duality mapping of is weakly sequentially continuous and 0 is in the range of , then for each in the strong <!-- MATH ${\lim _{r \to \infty }}{J_r}x$ --> exists and belongs to <!-- MATH ${A^{ - 1}}(0)$ --> . This is an extension to a Banach space setting of a result previously known only for Hilbert space.