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On the Mann iteration process in a Hilbert space. (English) Zbl 0361.65057

MSC:
65J05General theory of numerical methods in abstract spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
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References:
[1] Browder, F. E.; Petryshyn, W. V.: Construction of fixed points of nonlinear mappings in Hilbert spaces. J. math. Anal. appl. 20, 197-229 (1967) · Zbl 0153.45701
[2] Jr., W. G. Dotson: On the Mann iteration process. Trans. amer. Math. soc. 149, 65-73 (1970) · Zbl 0203.14801
[3] Franks, R. L.; Marzec, R. P.: A theorem on mean-value iterations. Proc. amer. Math. soc. 30, 324-326 (1971) · Zbl 0229.26005
[4] Goëbel, K.; Kirk, W. A.; Shimi, T. N.: A fixed point theorem in uniformily convex spaces. Boll. U.M.I. 7 (1973)
[5] Groetsch, C. W.: A note on segmenting Mann iteraties. J. math. Anal. appl. 40, 369-372 (1972) · Zbl 0244.47042
[6] Ishikawa, S.: Fixed points by a new iteration. Proc. amer. Math. soc. 44, 147-150 (1974) · Zbl 0286.47036
[7] Kannan, R.: Some results on fixed points. Bull. cal. Math. soc. 60, 71-76 (1968) · Zbl 0209.27104
[8] Kannan, R.: Some results on fixed points, II. Amer. math. Monthly 76, 405-408 (1969) · Zbl 0179.28203
[9] Kannan, R.: Some results on fixed points, III. Fund. math. 70, 160-177 (1971) · Zbl 0246.47065
[10] Kannan, R.: Some results on fixed points, IV. Fund. math. 74, 181-187 (1972) · Zbl 0257.54044
[11] Kannan, R.: Fixed point theorems in reflexive Banach spaces. Proc. amer. Math. soc. 38, 111-118 (1974) · Zbl 0265.47038
[12] Mann, W. R.: Mean value methods in iteration. Proc. amer. Math. soc. 4, 506-510 (1953) · Zbl 0050.11603
[13] Opial, Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. amer. Math. soc. 73, 591-597 (1967) · Zbl 0179.19902
[14] Outlaw, C.; Groetsch, C. W.: Averaging iteration in a Banach space. Bull. amer. Math. soc. 75, 430-432 (1969) · Zbl 0199.44903
[15] Petryshyn, W. V.; Jr., T. E. Williamson: Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings. J. math. Anal. appl. 43, 459-497 (1973) · Zbl 0262.47038
[16] Wong, C. S.: Fixed points and characterizations of certain maps. Pacific J. Math. 54, 305-312 (1974) · Zbl 0254.47075
[17] Reinermann, J.: Neue existenz-und konvergenzsätze in der fixpunkttheoric nichtlinearer operatoren. J. approx. Theory 8, 387-399 (1973) · Zbl 0276.47048