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Weak convergence of the sequence of successive approximations for nonexpansive mappings. (English) Zbl 0179.19902


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[1] Felix E. Browder, Fixed-point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1272 – 1276. · Zbl 0125.35801
[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] Felix E. Browder, Fixed point theorems for nonlinear semicontractive mappings in Banach spaces, Arch. Rational Mech. Anal. 21 (1966), 259 – 269. · Zbl 0144.39101 · doi:10.1007/BF00282247
[4] 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
[5] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004 – 1006. · Zbl 0141.32402 · doi:10.2307/2313345
[6] M. A. Krasnosel\(^{\prime}\)skiĭ, Two remarks on the method of successive approximations, Uspehi Mat. Nauk (N.S.) 10 (1955), no. 1(63), 123 – 127 (Russian).
[7] Helmut Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math. Verein. 59 (1957), no. Abt. 1, 131 – 140 (German). · Zbl 0077.11002
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