## 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

### MSC:

 47H06 Nonlinear accretive operators, dissipative operators, etc.
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### References:

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