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The mean-value iteration for set-valued mappings. (English) Zbl 0461.47030


MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)

Citations:

Zbl 0064.120
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Full Text: DOI

References:

[1] 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
[2] David Downing and W. A. Kirk, Fixed point theorems for set-valued mappings in metric and Banach spaces, Math. Japon. 22 (1977), no. 1, 99 – 112. · Zbl 0372.47030
[3] M. Edelstein, A remark on a theorem of M. A. Krasnoselski, Amer. Math. Monthly 73 (1966), 509 – 510. · Zbl 0138.39901 · doi:10.2307/2315474
[4] R. Kannan, Some results on fixed points. II, Amer. Math. Monthly 76 (1969), 405 – 408. · Zbl 0179.28203 · doi:10.2307/2316437
[5] 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).
[6] Teck Cheong Lim, A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space, Bull. Amer. Math. Soc. 80 (1974), 1123 – 1126. · Zbl 0297.47045
[7] W. Robert Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506 – 510. · Zbl 0050.11603
[8] Ernest Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152 – 182. · Zbl 0043.37902
[9] Sam B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475 – 488. · Zbl 0187.45002
[10] W. V. Petryshyn, Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl. 14 (1966), 276 – 284. · Zbl 0138.39802 · doi:10.1016/0022-247X(66)90027-8
[11] W. V. Petryshyn and T. E. Williamson Jr., Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings, J. Math. Anal. Appl. 43 (1973), 459 – 497. · Zbl 0262.47038 · doi:10.1016/0022-247X(73)90087-5
[12] Helmut Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math. Verein. 59 (1957), no. Abt. 1, 131 – 140 (German). · Zbl 0077.11002
[13] H. F. Senter and W. G. Dotson Jr., Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974), 375 – 380. · Zbl 0299.47032
[14] Chyi Shiau, Kok Keong Tan, and Chi Song Wong, Quasi-nonexpansive multi-valued maps and selections, Fund. Math. 87 (1975), 109 – 119. · Zbl 0307.54047
[15] Chyi Shiau, Kok Keong Tan, and Chi Song Wong, A class of quasi-nonexpansive multi-valued maps, Canad. Math. Bull. 18 (1975), no. 5, 709 – 714. · Zbl 0343.47045 · doi:10.4153/CMB-1975-124-2
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