Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces

[1] Atsushiba, Sachiko and Wataru Takahashi. “Nonlinear ergodic theorems without convexity for nonexpansive semigroups in Hilbert spaces.” J. Nonlinear Convex Anal. 14, no. 2 (2013): 209-219. Cited on 70.Search in Google Scholar

[2] Belluce, Lawrence P., and William A. Kirk. “Nonexpansive mappings and fixed-points in Banach spaces.” Illinois J. Math. 11 (1967): 474-479. Cited on 68.10.1215/ijm/1256054569Search in Google Scholar

[3] Berglund, John F., and Hugo D. Junghenn, and Paul Milnes. Analysis on semi-groups. New York: John Wiley & Sons, Inc., 1989. Cited on 73.Search in Google Scholar

[4] Brodskiĭ, M. S. and D. P. Mil’man. “On the center of a convex set.” Doklady Akad. Nauk SSSR (N.S.) 59 (1948): 837-840. Cited on 82.Search in Google Scholar

[5] Fan, Ky. “Minimax theorems.” Proc. Nat. Acad. Sci. U. S. A. 39, (1953): 42-47. Cited on 68.10.1073/pnas.39.1.42Search in Google Scholar

[6] Fan, Ky. “Existence theorems and extreme solutions for inequalities concerning convex functions or linear transformations.” Math. Z. 68 (1957): 205-216. Cited on 68 and 79.10.1007/BF01160340Search in Google Scholar

[7] Granirer, Edmond E. “On amenable semigroups with a finite-dimensional set of invariant means. I.” Illinois J. Math. 7 (1963): 32-48. Cited on 84.10.1215/ijm/1255637480Search in Google Scholar

[8] Granirer, Edmond E. “On amenable semigroups with a finite-dimensional set of invariant means. II.” Illinois J. Math. 7 (1963): 49-58. Cited on 84.10.1215/ijm/1255637481Search in Google Scholar

[9] Hewitt, Edwin and Kenneth A. Ross. Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations. Vol 115 of Die Grundlehren der mathematischen Wissenschaften, New York: Academic Press, Inc., 1963. Cited on 68.Search in Google Scholar

[10] Holmes, R. D., and Anthony To-Ming Lau. “Non-expansive actions of topological semigroups and fixed points.” J. London Math. Soc. 5, no. 2 (1972): 330-336. Cited on 69 and 84.10.1112/jlms/s2-5.2.330Search in Google Scholar

[11] Hsu, R. Topics on weakly almost periodic functions. Ph.D. diss., State University of New York at Buffalo, 1985. Cited on 70.Search in Google Scholar

[12] Lau, Anthomy To-Ming. “Invariant means on almost periodic functions and fixed point properties.” Rocky Mountain J. Math. 3 (1973): 69-76. Cited on 83.10.1216/RMJ-1973-3-1-69Search in Google Scholar

[13] Lau, Anthony To-Ming. “Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups.” Fund. Math. 118, no. 3 (1983): 161-175. Cited on 85.10.4064/fm-118-3-161-175Search in Google Scholar

[14] Lau, Anthony To-Ming. “Amenability and fixed point property for semigroup of nonexpansive mappings.” In Fixed point theory and applications (Marseille, 1989), 303–313. Vol. 252 of Pitman Res. Notes Math. Ser. Harlow: Longman Sci. Tech., 1991. Cited on 83 and 84.Search in Google Scholar

[15] Lau, Anthony To-Ming, and Wataru Takahashi. “Invariant submeans and semi-groups of nonexpansive mappings on Banach spaces with normal structure.” J. Funct. Anal. 142, no. 1 (1996): 79-88. Cited on 70.10.1006/jfan.1996.0144Search in Google Scholar

[16] Lau, Anthony To-Ming, and Wataru Takahashi. “Nonlinear submeans on semi-groups.” Topol. Methods Nonlinear Anal. 22, no. 2 (2003): 345-353. Cited on 70.10.12775/TMNA.2003.044Search in Google Scholar

[17] Lau, Anthony To-Ming, and Yong Zhang. “Fixed point properties of semigroups of non-expansive mappings.” J. Funct. Anal. 254, no. 10 (2008): 2534-2554. Cited on 83.10.1016/j.jfa.2008.02.006Search in Google Scholar

[18] Lau, Anthony To-Ming, and Yong Zhang. “Finite-dimensional invariant subspace property and amenability for a class of Banach algebras.” Trans. Amer. Math. Soc. 368, no. 6 (2016): 3755-3775. Cited on 85.10.1090/tran/6442Search in Google Scholar

[19] Lennard, Chris. C₁ is uniformly Kadec-Klee.” Proc. Amer. Math. Soc. 109, no. 1 (1990): 71-77. Cited on 68.10.1090/S0002-9939-1990-0943795-4Search in Google Scholar

[20] Lim, Teck Cheong. “Asymptotic centers and nonexpansive mappings in conjugate Banach spaces.” Pacific J. Math. 90, no. 1 (1980) 135-143. Cited on 69 and 70.10.2140/pjm.1980.90.135Search in Google Scholar

[21] Lim, Teck Cheong. “Characterizations of normal structure.” Proc. Amer. Math. Soc. 43 (1974): 313-319. Cited on 69.10.1090/S0002-9939-1974-0361728-XSearch in Google Scholar

[22] Lim, Teck Cheong. “A fixed point theorem for families on nonexpansive mappings.” Pacific J. Math. 53: (1974) 487-493. Cited on 80.10.2140/pjm.1974.53.487Search in Google Scholar

[23] Mizoguchi, Noriko, and Wataru Takahashi. “On the existence of fixed points and ergodic retractions for Lipschitzian semigroups in Hilbert spaces.” Nonlinear Anal. 14, no. 1 (1990): 69-80. Cited on 70.10.1016/0362-546X(90)90136-5Search in Google Scholar

[24] Randrianantoanina, Narcisse. “Fixed point properties of semigroups of nonexpansive mappings.” J. Funct. Anal. 258, no. 11 (2010): 3801-3817. Cited on 68.10.1016/j.jfa.2010.01.022Search in Google Scholar

[25] Wiśnicki, Andrzej. “Amenable semigroups of nonexpansive mappings on weakly compact convex sets.” J. Nonlinear Convex Anal. 17, no. 10 (2016): 2119-2127. Cited on 68.Search in Google Scholar