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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 \[ x^{n+1}=x^n-\varepsilon_n (A^{h_n} x^n+ \alpha_n x^n), \] \(\text{dist}(A^h x, Ax) \leq g(\| x\|)h,\) \(\varepsilon_n>0\), \(\alpha_n>0\) for solving the inclusion \(0 \in Ax\) with an accretive multivalued operator \(A: B \to B\) in a Banach space \(B\) [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.

MSC:
47H06 Nonlinear accretive operators, dissipative operators, etc.
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J05 Equations involving nonlinear operators (general)
47J25 Iterative procedures involving nonlinear operators
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