An asymptotically nonexpansive commutative semigroup with no fixed points

Tingley, Daryl

doi:10.1090/S0002-9939-1986-0831397-9

An asymptotically nonexpansive commutative semigroup with no fixed points
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Proc. Amer. Math. Soc. 97 (1986), 107-113 Request permission

Abstract:

An example of an asymptotically nonexpansive commutative semigroup with no fixed points is presented.

References

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. MR 190744, DOI 10.1090/S0002-9904-1966-11543-4
Ralph DeMarr, Common fixed points for commuting contraction mappings, Pacific J. Math. 13 (1963), 1139–1141. MR 159229
Michael Edelstein, On non-expansive mappings of Banach spaces, Proc. Cambridge Philos. Soc. 60 (1964), 439–447. MR 164222
Michael Edelstein, Fixed point theorems in uniformly convex Banach spaces, Proc. Amer. Math. Soc. 44 (1974), 369–374. MR 358451, DOI 10.1090/S0002-9939-1974-0358451-4
Michael Edelstein and Mo Tak Kiang, On ultimately nonexpansive semigroups, Pacific J. Math. 101 (1982), no. 1, 93–102. MR 671841
Michael Edelstein and Richard C. O’Brien, Nonexpansive mappings, asymptotic regularity and successive approximations, J. London Math. Soc. (2) 17 (1978), no. 3, 547–554. MR 500642, DOI 10.1112/jlms/s2-17.3.547
K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174. MR 298500, DOI 10.1090/S0002-9939-1972-0298500-3
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
Mo Tak Kiang, Fixed point theorems for certain classes of semigroups of mappings, Trans. Amer. Math. Soc. 189 (1974), 63–76. MR 361949, DOI 10.1090/S0002-9947-1974-0361949-0
Teck Cheong Lim, A fixed point theorem for families on nonexpansive mappings, Pacific J. Math. 53 (1974), 487–493. MR 365250
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. MR 394333, DOI 10.1090/S0002-9904-1974-13640-2

Introduction to the theory of basis

C. W. McArthur, Ivan Singer, and Mark Levin, On the cones associated with biorthogonal systems and bases in Banach spaces, Canadian J. Math. 21 (1969), 1206–1217. MR 259569, DOI 10.4153/CJM-1969-133-7
Daryl Tingley, The construction of a fixed point for certain families of mappings, Applicable Anal. 17 (1984), no. 3, 187–192. MR 750891, DOI 10.1080/00036818408839494