Approximating zeros of accretive operators

Reich, Simeon

doi:10.1090/S0002-9939-1975-0470762-1

Approximating zeros of accretive operators
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Proc. Amer. Math. Soc. 51 (1975), 381-384 Request permission

Abstract:

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

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