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Approximating fixed points of nonexpansive mappings. (English) Zbl 0299.47032


MSC:

47H10 Fixed-point theorems
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[1] Felix E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041 – 1044. · Zbl 0128.35801
[2] 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
[3] W. G. Dotson Jr., Fixed points of quasi-nonexpansive mappings, J. Austral. Math. Soc. 13 (1972), 167 – 170. · Zbl 0227.47047
[4] W. G. Dotson Jr., On the Mann iterative process, Trans. Amer. Math. Soc. 149 (1970), 65 – 73. · Zbl 0203.14801
[5] C. W. Groetsch, A note on segmenting Mann iterates, J. Math. Anal. Appl. 40 (1972), 369 – 372. · Zbl 0244.47042
[6] R. Kannan, Some results on fixed points. III, Fund. Math. 70 (1971), no. 2, 169 – 177. · Zbl 0246.47065
[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] W. Robert Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506 – 510. · Zbl 0050.11603
[9] Z. Opial, Nonexpansive and monotone mappings in Banach spaces, Center for Dynamical Systems, Division of Applied Math., Brown University, Lecture Notes 67-1, 1967.
[10] Curtis L. Outlaw, Mean value iteration of nonexpansive mappings in a Banach space, Pacific J. Math. 30 (1969), 747 – 750. · Zbl 0179.19801
[11] W. V. Petryshyn, Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl. 14 (1966), 276 – 284. · Zbl 0138.39802
[12] Simeon Reich, Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121 – 124. · Zbl 0211.26002
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