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Common fixed points of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach space. (English) Zbl 1161.65043
The main purpose of the paper is to study the following iteration scheme: $$ y_{n}=P(1-\beta_{n})x_{n}+\beta_{n}T_{2}(PT_{2})^{n-1}x_{n},\quad x_{n+1}=P(1-\alpha_{n})y_{n}+\alpha_{n}T_{1}(PT_{1})^{n-1}y_{n}, $$ where $X$ is a normed space, $C$ a convex nonempty subset $P:X\rightarrow C$ a nonexpensive retraction of $X$ onto $C$ , $T_{1}, T_{2}: C \rightarrow X $ given mappings. The last two theorems yield conditions under which the sequences are weakly respectively strongly convergent.

MSC:
65J15Equations with nonlinear operators (numerical methods)
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
46B20Geometry and structure of normed linear spaces
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References:
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