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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 $$x_{n+1}=(1-\alpha _n)x_n+\alpha _nT^nx_n$$, $$n\in \mathbb N$$, 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:
 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 46B20 Geometry and structure of normed linear spaces 47H10 Fixed-point theorems
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