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On nonexpansive mappings. (English) Zbl 0328.47033

MSC:
47H10 Fixed-point theorems
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[1] Garrett Birkhoff, Orthogonality in linear metric spaces, Duke Math. J. 1 (1935), no. 2, 169 – 172. · Zbl 0012.30604
[2] Felix E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041 – 1044. · Zbl 0128.35801
[3] F. E. Browder and W. V. Petryshyn, The solution by iteration of linear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 566 – 570. , https://doi.org/10.1090/S0002-9904-1966-11543-4 F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 571 – 575. · Zbl 0138.08201
[4] Dietrich Göhde, Über Fixpunkte bei stetigen Selbstabbildungen mit kompakten Iterierten, Math. Nachr. 28 (1964), 45 – 55 (German). · Zbl 0139.31402
[5] Robert C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc. 61 (1947), 265 – 292. · Zbl 0037.08001
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[7] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004 – 1006. · Zbl 0141.32402
[8] J. Lindenstrauss and C. Stegall, Examples of spaces which do not contain \( {l_1}\) and whose duals are not separable (to appear). · Zbl 0324.46017
[9] Zdzisław Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591 – 597. · Zbl 0179.19902
[10] L. P. Belluce, W. A. Kirk, and E. F. Steiner, Normal structure in Banach spaces, Pacific J. Math. 26 (1968), 433 – 440. · Zbl 0164.15001
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