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Zbl 0712.47045
Ha, Ki Sik; Jung, Jong Soo
Strong convergence theorems for accretive operators in Banach spaces.
(English)
[J] J. Math. Anal. Appl. 147, No.2, 330-339 (1990). ISSN 0022-247X

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) $\lim\sb{t\downarrow 0}(I+tA)\sp{-1}x$ exists, and (ii) if R(A) contains 0, then $\lim\sb{t\to +\infty}(I+tA)\sp{-1}$ exists and belongs to $A\sp{(-1)}(0).$ \par 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).
[T.Ichinose]
MSC 2000:
*47H06 Accretive operators, etc. (nonlinear)

Keywords: nonlinear m-accretive operator; Banach space with a uniformly Gâteaux differentiable norm; nonexpansive retraction

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