Approximating fixed points of nonexpansive mappings in a Banach space by metric projections. (English) Zbl 1190.47072
Summary: A strong convergence theorem for nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem is different from the recent strong convergence theorem due to H.-K.Xu [Bull.Aust.Math.Soc.74, No.1, 143–151 (2006; Zbl 1126.47056)] which was established by generalized projections.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H10 | Fixed-point theorems |
Keywords:
nonexpansive mapping; metric projection; uniformly convex Banach space; fixed point approximationCitations:
Zbl 1126.47056References:
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