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Convergence theorems for nonexpansive mappings and feasibility problems. (English) Zbl 0971.47040
The authors introduce an iteration scheme given by finite nonexpansive mappings in Banach spaces and prove some convergence theorems which are connected with the problem of image recovery. Using these results, they study common fixed points of finite nonexpansive operators.

47H09Mappings defined by “shrinking” properties
47J25Iterative procedures (nonlinear operator equations)
65J15Equations with nonlinear operators (numerical methods)
Full Text: DOI
[1] Crombez, G.: Image recovery by convex combinations of projections. J. math. Anal. appl. 155, 413-419 (1991) · Zbl 0752.65045
[2] Kitahara, S.; Takahashi, W.: Image recovery by convex combinations for sunny nonexpansive retractions. Topol. methods nonlinear anal. 2, 333-342 (1993) · Zbl 0815.47068
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[13] W. Takahashi and G.E. Kim, Approximating fixed points of nonexpansive mappings in Banach spaces, Math. Japonica (to appear). · Zbl 0913.47056
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