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A strong convergence theorem for contraction semigroups in Banach spaces. (English) Zbl 1095.47016

T. Suzuki in [Proc. Am. Math. Soc. 131, No. 7, 2133–2136 (2003; Zbl 1031.47038)] established a theorem on the strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces. In the paper under review, the author generalizes Suzuki’s result for uniformly convex Banach spaces with a weakly continuous duality map.

MSC:

47H20 Semigroups of nonlinear operators
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Citations:

Zbl 1031.47038
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References:

[1] Goebel, Uniform convexity, hyperbolic geometry, and nonexpansive mappings (1984) · Zbl 0537.46001
[2] DOI: 10.1007/BF02764907 · Zbl 0423.47024
[3] DOI: 10.1007/BF01109805 · Zbl 0149.36301
[4] Browder, Fixed point theorems for noncompact mappings in Hilbert space 53 pp 1272– (1965) · Zbl 0125.35801
[5] DOI: 10.1016/0362-546X(94)90116-3 · Zbl 0812.47058
[6] DOI: 10.1112/S0024610702003332 · Zbl 1013.47032
[7] DOI: 10.1090/S0002-9939-02-06844-2 · Zbl 1031.47038
[8] DOI: 10.1016/S0362-546X(97)00682-2 · Zbl 0935.47039
[9] DOI: 10.1016/0022-247X(80)90323-6 · Zbl 0437.47047
[10] DOI: 10.1080/01630569808816821 · Zbl 0908.47057
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