zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Fixed point properties for semigroup of nonexpansive mappings on Fréchet spaces. (English) Zbl 1219.47082
Authors’ abstract: We establish a fixed point property on Fréchet spaces for left reversible semitopological semigroups, generalizing some classical results.

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H20Semigroups of nonlinear operators
Full Text: DOI
[1] Alspach, D.: A fixed point free nonexpansive map. Proc. amer. Math. soc. 82, 423-424 (1981) · Zbl 0468.47036
[2] Berglund, J. F.; Junghenn, H. D.; Milnes, P.: Analysis on semigroups. (1989) · Zbl 0727.22001
[3] Clifford, A. H.; Preston, G. B.: The algebraic theory of semigroups. 1 (1961) · Zbl 0111.03403
[4] Demarr, R.: Common fixed points for commuting contractive mappings. Pacific J. Math. 13, 1139-1141 (1963) · Zbl 0191.14901
[5] Holmes, R. D.; Lau, A. T.: Semigroups and fixed points. J. London math. Soc. 5, 330-336 (1972) · Zbl 0248.47029
[6] Lau, A. T.; Miyake, H.; Takahashi, W.: Approximation of fixed points for amenable semigroups of nonexpansive mappings in Banach spaces. Nonlinear anal. 67, 1211-1225 (2007) · Zbl 1123.47048
[7] Lau, A. T.; Takahashi, W.: Invariant means and semigroups of nonexpansive mappings on uniformly convex Banach spaces. J. math. Anal. appl. 153, 497-505 (1990) · Zbl 0782.47034
[8] Lau, A. T.; Takahashi, W.: Invariant means and fixed point properties for non-expansive representations of topological semigroups. Topol. methods nonlinear anal. 5, 39-57 (1995) · Zbl 0834.43001
[9] Lau, A. T.; Takahashi, W.: Invariant submeans and semigroups of nonexpansive mappings on Banach spaces with normal structure. J. funct. Anal. 142, 79-88 (1996) · Zbl 0862.43001
[10] Lau, A. T.; Takahashi, W.: Nonlinear submeans on semigroups. Topol. methods nonlinear anal. 22, 345-353 (2003) · Zbl 1039.43002
[11] Lau, A. T.; Zhang, Y.: Fixed point properties of semigroups of non-expansive mappings. J. funct. Anal. 254, 2534-2554 (2008) · Zbl 1149.47046
[12] Lim, T. C.: Asymptotic centers and nonexpansive mappings in conjugate Banach space. Pacific J. Math. 90, 135-143 (1980) · Zbl 0454.47046
[13] Mitchell, T.: Topological semigroups and fixed points. Illinois J. Math. 14, 630-641 (1970) · Zbl 0219.22003
[14] Mitchell, T.: Fixed points of reversible semigroups of non-expansive mappings. Kodai math. Sem. rep. 22, 322-323 (1970) · Zbl 0224.47020
[15] Namioka, I.: Neighborhoods of extreme points. Israel J. Math. 5, 145-152 (1967) · Zbl 0177.40501
[16] Takahashi, W.: Fixed point theorem for amenable semigroup of nonexpansive mappings. Kodai math. Sem. rep. 21, 383-386 (1969) · Zbl 0197.11805
[17] Takahashi, W.; Jeong, D. H.: Fixed point theorem for nonexpansive semigroups on Banach space. Proc. amer. Math. soc. 122, 1175-1179 (1994) · Zbl 0818.47055