Strong convergence of resolvents of monotone operators in Banach spaces

Abstract:

Let ${E^*}$ be a real strictly convex dual Banach space with a Fréchet differentiable norm, and $A$ a maximal monotone operator from $E$ into ${E^*}$ such that ${A^{ - 1}}0 \ne \emptyset$. Fix $x \in E$. Then ${J_\lambda }x$ converges strongly to $Px$ as $\lambda \to \infty$, where ${J_\lambda }$ is the resolvent of $A$, and $P$ is the nearest point mapping from $E$ onto ${A^{ - 1}}0$.