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

For a nonlinear m-accretive operator AE×E with domain D(A) and range R(A) in a real Hilbert space E, it is known that for each xE, (i) lim t0 (I+tA) -1 x exists, and (ii) if R(A) contains 0, then lim t+ (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:
47H06Accretive operators, dissipative operators, etc. (nonlinear)