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Asymptotically strict pseudocontractive mappings in the intermediate sense. (English) Zbl 1221.47122
Summary: It is proved that the modified Mann iteration process $x_{n+1}=(1-\alpha _n)x_n+\alpha _nT^nx_n$, $n\in \Bbb N$, where $\{\alpha _n\}$ is a sequence in (0,1) with $\delta \leq \alpha _n\leq 1 - \kappa - \delta $ for some $\delta \in (0,1)$, converges weakly to a fixed point of an asymptotically $\kappa $-strict pseudocontractive mapping $T$ in the intermediate sense which is not necessarily Lipschitzian. We also develop a CQ method for this modified Mann iteration process which generates a strongly convergent sequence.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
46B20Geometry and structure of normed linear spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
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Full Text: DOI
References:
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