Krasnoselski-Mann Iterations in Normed Spaces
Canadian mathematical bulletin, Tome 35 (1992) no. 1, pp. 21-28

Voir la notice de l'article provenant de la source Cambridge University Press

We provide general results on the behaviour of the Krasnoselski-Mann iteration process for nonexpansive mappings in a variety of normed settings.
DOI : 10.4153/CMB-1992-003-0
Mots-clés : 47H09, 47H10, 47H17.
Borwein, Jonathan; Reich, Simeon; Shafrir, Itai. Krasnoselski-Mann Iterations in Normed Spaces. Canadian mathematical bulletin, Tome 35 (1992) no. 1, pp. 21-28. doi: 10.4153/CMB-1992-003-0
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[1] 1. Dotson, W. G., On the Mann iterative process, Trans. Amer. Math. Soc. 149(1970),655–73. Google Scholar

[2] 2. Edelstein, M. and R. C. O'Brien Nonexpansive mappings, asymptotic regularity and successive approximations, J. London Math. Soc. 17(1978),547–554. Google Scholar

[3] 3. Fujihara, T., Asymptotic behavior of nonexpansive mappings in Banach spaces, Tokyo J. Math. 7(1984),119–128. Google Scholar

[4] 4. Goebel, K., and Kirk, W. A., Iteration processes for nonexpansive mappings, Contemporary Mathematics 21(1983),115–123. Google Scholar

[5] 5. Groetsch, C.W., A note on segmenting Mann iterates, J. Math. Anal, and Appl. 40(1972),369–372. Google Scholar

[6] 6. Hicks, T. L. and Kubicek, J. D., On the Mann iteration process in Hilbert space, J. Math. Anal, and Appl. 59(1977),498–504. Google Scholar

[7] 7. Hillam, B. P., A generalization ofKrasnoselski s theorem on the real line, Mathematics Magazine 48( 1975), 167–168. Google Scholar

[8] 8. Ishikawa, S., Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59(1976),65–71. Google Scholar

[9] 9. Kirk, W. A., KrasnoselskiVs iteration process in hyperbolic space, Numer. Funct. Anal. Optimiz. 4(1982),371–381. Google Scholar

[10] 10. Kirk, W. A., Fixed point theory for nonexpansive mappings, I and II, (I) appears in Lecture Notes in Mathematics 886 (Springer-Verlag, 1981), pp. 484-505; (II) appears in: Fixed Points and Nonexpansive Mappings (R. Sine, éd.), Contemporary Math. 18, Amer. Math. Soc, Providence RI, (1983), pp. 121–140. Google Scholar

[11] 11. Kohlberg, E., and Neyman, A., Asymptotic behaviour of nonexpansive mappings in normed linear spaces, Israel J. Math. 38(1981),269–275. Google Scholar

[12] 12. Krasnoselski, M. A., Two observations about the method of successive approximations, Usp. Math. Nauk, 10(1955),123–127. Google Scholar

[13] 13. Mann, W. R., Mean value methods in iteration, Proc. Amer. Math. Soc. 4(1953),506–510. Google Scholar

[14] 14. Reich, S., On the asymptotic behaviour of nonlinear semigroups and the range of accretive operators II, J. Math. Anal. Appl. 87(1982),134–146. Google Scholar

[15] 15. Reich, S., Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 67(1979),274–276. Google Scholar

[16] 16. Reich, S., The almost fixed point property for nonexpansive mappings, Proc. Amer. Math. Soc. 88(1983),44–45. Google Scholar

[17] 17. Reich, S. and Shafrir, I., On the method of successive approximationsfor nonexpansive mappings, Nonlinear and Convex Analysis, Marcel Dekker, New York, (1987), 193–201. Google Scholar

[18] 18. Reich, S. and Shafrir, I., Nonexpansive iterations in hyperbolic spaces, Nonlinear Analysis 15(1990),537–558. Google Scholar

[19] 19. Shafrir, I., The approximate fixed point property in Banach and hyperbolic spaces, Israel J. Math, 71( 1990), 211–223. Google Scholar

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