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Construction of fixed points of a class of nonlinear mappings. (English) Zbl 0261.47037

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
54H25Fixed-point and coincidence theorems in topological spaces
Full Text: DOI
[1] Browder, F. E.: Nonexpansive nonlinear operators in a Banach space. Proc. nat. Acad. sci. 54, 1041-1044 (1965) · Zbl 0128.35801
[2] Browder, F. E.; Petryshyn, W. V.: The solution by iteration of nonlinear functional equations in Banach spaces. Bull. amer. Math. soc. 72, 571-575 (1966) · Zbl 0138.08202
[3] Danes, J.: Some fixed point theorems in metric and Banach spaces. Comment. math. Univ. carolinae 12, 37-52 (1971)
[4] Edelstein, M.: A remark on a theorem of M.A. Krasnoselskii. Amer. math. Monthly 73, 509-510 (1966) · Zbl 0138.39901
[5] Gohde, D.: Zum prinzip der kontraktiven abbildung. Math. nach. 30, 251-258 (1965) · Zbl 0127.08005
[6] Kannan, R.: Some results on fixed points. Bull. Calcutta math. Soc. 60, 71-76 (1968) · Zbl 0209.27104
[7] Kannan, R.: Some results on fixed points--II. Amer. math. Monthly 76, 405-408 (1969) · Zbl 0179.28203
[8] Kannan, R.: Some results on fixed points--III. Fund. math. 70, 169-177 (1971) · Zbl 0246.47065
[9] Kannan, R.: Some results on fixed points--IV. Fund. math. 74, 181-187 (1972) · Zbl 0257.54044
[10] R. Kannan, Fixed point theorems in reflexive Banach spaces, to appear in Proc. Amer. Math. Soc. · Zbl 0265.47038
[11] Kirk, W. A.: A fixed point theorem for mappings which do not increase distances. Amer. math. Montly 72, 1004-1006 (1965) · Zbl 0141.32402
[12] Kirk, W. A.: On successive approximations for nonexpansive mappings in Banach spaces. Glasgow math. J. 12, 6-9 (1971) · Zbl 0223.47024
[13] Krasnoselskii, M. A.: Two remarks about the method of successive approximations. Uspehi. math. Nauk 10, 123-127 (1955)
[14] Petryshyn, W. V.: Construction of fixed points for demicompact mappings in Hilbert space. J. of math. Anal. appl. 14, 276-284 (1966) · Zbl 0138.39802
[15] Reich, S.: Kannan’s fixed point theorem. Boll. unione. Math. Italy 4, 1-11 (1971) · Zbl 0219.54042
[16] Schaefer, H.: Über die methode suksessiver approximation. Jber. deutsch. Math.-verein 59, 131-140 (1957) · Zbl 0077.11002