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Fixed point theorems for Lipschitzian mappings in Banach spaces. (English) Zbl 0856.47031
In this interesting paper, the authors prove some new results in the fixed point theory for asymptotically nonexpansive maps and geometry of Banach spaces. For example, they essentially strengthen a classical fixed point theorem of K. Goebel [Compos. Math. 22, 269-274 (1970; Zbl 0202.12802)] for Lipschitz operators on weakly compact convex sets.
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
Full Text: DOI
[1] Goebel, K.; Kirk, W.A., Topics in metric fixed point theory, (1990), Cambridge University Press New York · Zbl 0708.47031
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[13] Goebel, K.; Koter, M., A remark on nonexpansive mappings, Can. math. bull., 24, 113-115, (1981) · Zbl 0461.47027
[14] Kirk, W.A., A fixed point theorem for mappings of asymptotically nonexpansive type, Israel J. math., 17, 339-346, (1974) · Zbl 0286.47034
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