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Approximation for fixed points of asymptotically nonexpansive mappings. (English) Zbl 0734.47037
The author studies the convergence of the iteration sequence z n+1 =μ n+1 T n (z n ), where T is an asymptotically nonexpansive self-mapping of a nonempty closed, bounded, and starshaped subset of a smooth reflexive Banach space. Related previous work is due to K. Goebel, B. Halpern, W. A. Kirk, and P. Vijayaraju [e.g. Bull. Calcutta Math. Soc. 80, No.2, 133-136 (1988; Zbl 0667.47032)].
MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties