Strong convergence theorems for accretive operators in Banach spaces. (English) Zbl 0712.47045

For a nonlinear m-accretive operator \(A\subset E\times E\) with domain D(A) and range R(A) in a real Hilbert space E, it is known that for each \(x\in E\), (i) \(\lim_{t\downarrow 0}(I+tA)^{-1}x\) exists, and (ii) if R(A) contains 0, then \(\lim_{t\to +\infty}(I+tA)^{-1}\) exists and belongs to \(A^{(-1)}(0).\)
The paper under review extends the assertions (i) and (ii) to the case where E is a real reflexive Banach space with a uniformly Gâteaux differentiable norm, and \(I+tA\) is replaced by \(S+tA\) with S a bounded, strongly accretive and continuous operator of the closure of D(A) into E, assuming existence of a nonexpansive retraction of E onto the closure of D(A).
Reviewer: T.Ichinose


47H06 Nonlinear accretive operators, dissipative operators, etc.
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