Geodesic
Fixed Point Theorems for Proximately Nonexpansive Semigroups
Canadian mathematical bulletin, Tome 29 (1986) no. 2, pp. 160-166

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

A commutative semigroup G of continuous, selfmappings on (X, d) is called proximately nonexpansive on X if for every x in X and every (β > 0, there is a member g in G such that d(fg(x),fg(y)) ≤ (1 + β) d (x, y) for every f in G and y in X. For a uniformly convex Banach space it is shown that if G is a commutative semigroup of continuous selfmappings on X which is proximately nonexpansive, then a common fixed point exists if there is an x0 in X such that its orbit G(x0) is bounded. Furthermore, the asymptotic center of G(x0) is such a common fixed point.
DOI : 10.4153/CMB-1986-027-2
Mots-clés : 47H10, Common fixed point, proximately nonexpansive, asymptotic center 
Kiang, Mo Tak; Tan, Kok-Keong. Fixed Point Theorems for Proximately Nonexpansive Semigroups. Canadian mathematical bulletin, Tome 29 (1986) no. 2, pp. 160-166. doi: 10.4153/CMB-1986-027-2
@article{10_4153_CMB_1986_027_2,
     author = {Kiang, Mo Tak and Tan, Kok-Keong},
     title = {Fixed {Point} {Theorems} for {Proximately} {Nonexpansive} {Semigroups}},
     journal = {Canadian mathematical bulletin},
     pages = {160--166},
     year = {1986},
     volume = {29},
     number = {2},
     doi = {10.4153/CMB-1986-027-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-027-2/}
}
TY  - JOUR
AU  - Kiang, Mo Tak
AU  - Tan, Kok-Keong
TI  - Fixed Point Theorems for Proximately Nonexpansive Semigroups
JO  - Canadian mathematical bulletin
PY  - 1986
SP  - 160
EP  - 166
VL  - 29
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-027-2/
DO  - 10.4153/CMB-1986-027-2
ID  - 10_4153_CMB_1986_027_2
ER  - 
%0 Journal Article
%A Kiang, Mo Tak
%A Tan, Kok-Keong
%T Fixed Point Theorems for Proximately Nonexpansive Semigroups
%J Canadian mathematical bulletin
%D 1986
%P 160-166
%V 29
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-027-2/
%R 10.4153/CMB-1986-027-2
%F 10_4153_CMB_1986_027_2

[1] 1. Browder, F.E., Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A., 54(1965), pp. 1041–1044. Google Scholar

[2] 2. Edelstein, M., The construction of an asymptotic center with a fixed point property, Bull. Amer. Math Soc, 78(1972), pp. 206–208. Google Scholar

[3] 3. Edelstein, M., On a fixed-point property of a reflexive, locally uniformly convex Banach space, C.R. Math Rep. Acad. Sci. Canada, 4 (1982), pp. 111–116. Google Scholar

[4] 4. Edelstein, M. and Kiang, M.T., On ultimately nonexpansive semigroups, Pac. J. of Math., 101 (1982), pp. 93–102. Google Scholar

[5] 5. Gôhde, D., Zum prinzip der kontraktiven Abbildung, Math. Nachr., 30 (1965), pp. 251–258. Google Scholar

[6] 6. Goebel, K. and Kirk, W.A., A fixed point theorem for asymptotically-nonexpansive mappings, Proc. Amer. Math Soc, 35 (1972), pp. 171–174. Google Scholar

[7] 7. Goebel, K. and Reich, S., “Uniform Convexity, Hyperbolic Geometry and Nonexpansive mappings”, Marcel Dekker, New York, 1984. Google Scholar

[8] 8. Kirk, W.A., Fixed point theory for nonexpansive mappings II, Contemporary Mathematics, Vol. 18 (1983), pp. 121–140. Google Scholar

[9] 9. Reich, S., The fixed point property for nonexpansive mappings I, II, Amer. Math. Monthly, 83 (1976), pp. 266–268. 87 (1980), pp. 292-294. Google Scholar

[10] 10. Tingley, D., An asymptotically nonexpansive commutative semigroup with no fixed points, (to appear). Google Scholar

Cité par Sources :