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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 \(z_{n+1}=\mu_{n+1}T^ n(z_ n),\) 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)].

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
Full Text: DOI
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[2] Joseph Diestel, Geometry of Banach spaces — selected topics, Lecture Notes in Mathematics, Vol. 485, Springer-Verlag, Berlin-New York, 1975. · Zbl 0307.46009
[3] K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171 – 174. · Zbl 0256.47045
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[7] P. Vijayaraju, Fixed point theorems for asymptotically nonexpansive mappings, Bull. Calcutta Math. Soc. 80 (1988), no. 2, 133 – 136. · Zbl 0667.47032
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