Fixed point theorems for certain classes of semigroups of mappings

Kiang, Mo Tak

doi:10.1090/S0002-9947-1974-0361949-0

Fixed point theorems for certain classes of semigroups of mappings
HTML articles powered by AMS MathViewer

by Mo Tak Kiang PDF

Trans. Amer. Math. Soc. 189 (1974), 63-76 Request permission

Abstract:

Fixed point theorems for commuting semigroups of self-mappings are considered in this paper. A generalization of the classical Markov-Kakutani theorem is first given. This is followed by a fixed point theorem for commutative semigroups of continuous asymptotically-nonexpansive self-mappings on a weakly compact, convex subset of a strictly convex Banach space.

References

M. S. Brodskiĭ and D. P. Mil′man, On the center of a convex set, Doklady Akad. Nauk SSSR (N.S.) 59 (1948), 837–840 (Russian). MR 0024073
Ralph DeMarr, Common fixed points for commuting contraction mappings, Pacific J. Math. 13 (1963), 1139–1141. MR 159229, DOI 10.2140/pjm.1963.13.1139
Michael Edelstein, On non-expansive mappings of Banach spaces, Proc. Cambridge Philos. Soc. 60 (1964), 439–447. MR 164222, DOI 10.1017/S0305004100037956

A generalization of a theorem of De Marr

R. D. Holmes and Anthony T. Lau, Non-expansive actions of topological semigroups and fixed points, J. London Math. Soc. (2) 5 (1972), 330–336. MR 313895, DOI 10.1112/jlms/s2-5.2.330
R. D. Holmes and P. P. Narayanaswamy, On asymptotically nonexpansive semigroups of mappings, Canad. Math. Bull. 13 (1970), 209–214. MR 266188, DOI 10.4153/CMB-1970-042-1
Shizuo Kakutani, Two fixed-point theorems concerning bicompact convex sets, Proc. Imp. Acad. Tokyo 14 (1938), no. 7, 242–245. MR 1568507

Quelques théorèmes sur les ensembles abéliens

10