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Strong Convergence of Resolvents of Monotone Operators in Banach Spaces

Strong Convergence of Resolvents of Monotone Operators in Banach Spaces

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_10 # 0. Fix x € E. Then J\x converges strongly to Px as A -► oo, where J\ is the resolvent