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Zbl 1051.47041
Chidume, C. E.; Zegeye, H.
Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps.
(English)
[J] Proc. Am. Math. Soc. 132, No. 3, 831-840 (2004). ISSN 0002-9939; ISSN 1088-6826/e

The presented results mainly follow from the proof of Al'ber's theorem concerning the process $$x^{n+1}=x^n-\varepsilon_n (A^{h_n} x^n+ \alpha_n x^n),$$ $\text{dist}(A^h x, Ax) \leq g(\Vert x\Vert)h,$ $\varepsilon_n>0$, $\alpha_n>0$ for solving the inclusion $0 \in Ax$ with an accretive multivalued operator $A: B \to B$ in a Banach space $B$ [{\it Ya. I. Al'ber}, Sov. Math. 30, No. 4, 1--8 (1986); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No. 4 (287), 3--8 (1986; Zbl 0623.47071)]. Unfortunately, the authors do not refer to Al'ber's works.
[Mikhail Yu. Kokurin (Yoshkar-Ola)]
MSC 2000:
*47H06 Accretive operators, etc. (nonlinear)
47H09 Mappings defined by "shrinking" properties
47J05 Equations involving nonlinear operators (general)
47J25 Methods for solving nonlinear operator equations (general)

Keywords: accretive multivalued operator; Banach space; operator inclusion; iterative process

Citations: Zbl 0623.47071

Cited in: Zbl 1192.47057

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