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Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps. (English) Zbl 1051.47041
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.

47H06Accretive operators, dissipative operators, etc. (nonlinear)
47H09Mappings defined by “shrinking” properties
47J05Equations involving nonlinear operators (general)
47J25Iterative procedures (nonlinear operator equations)
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