Geodesic
Nonexpansive Mappings in Locally Convex Spaces
Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 455-461

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

Recently Bruck initiated the study of the structure of the fixed-point set of a nonexpansive selfmap T of a Banach space, where T satisfies a conditional fixed point property. We generalize many of his results to a Hausdorff locally convex space X. Also, we generalize a result of Holmes and Narayanaswami and use it, along with a procedure of Kiang, to obtain a fixed point theorem for families of asymptotically nonexpansive mappings in X. 
Hicks, Troy L.; Kubicek, John D. Nonexpansive Mappings in Locally Convex Spaces. Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 455-461. doi: 10.4153/CMB-1977-067-9
@article{10_4153_CMB_1977_067_9,
     author = {Hicks, Troy L. and Kubicek, John D.},
     title = {Nonexpansive {Mappings} in {Locally} {Convex} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {455--461},
     year = {1977},
     volume = {20},
     number = {4},
     doi = {10.4153/CMB-1977-067-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-067-9/}
}
TY  - JOUR
AU  - Hicks, Troy L.
AU  - Kubicek, John D.
TI  - Nonexpansive Mappings in Locally Convex Spaces
JO  - Canadian mathematical bulletin
PY  - 1977
SP  - 455
EP  - 461
VL  - 20
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-067-9/
DO  - 10.4153/CMB-1977-067-9
ID  - 10_4153_CMB_1977_067_9
ER  - 
%0 Journal Article
%A Hicks, Troy L.
%A Kubicek, John D.
%T Nonexpansive Mappings in Locally Convex Spaces
%J Canadian mathematical bulletin
%D 1977
%P 455-461
%V 20
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-067-9/
%R 10.4153/CMB-1977-067-9
%F 10_4153_CMB_1977_067_9

[1] 1. Antonovskii, M.Y., Boltyanskii, V.G. and Sarymsakov, T.A., An outline of the tsheory of topological semi-fields, Russian Math. Surveys, 21 (1966), 163-192. Google Scholar

[2] 2. Bruck, R.E., Properties of fixed point sets of nonexpansive mappings in Banach spaces, Trans. Amer. Math. Soc, 179 (1973), 251-262. Google Scholar

[3] 3. Holmes, R.D. and Narayanaswami, P.P., On asymptotically nonexpansive semigroups of mappings, Can. Math. Bull., 13 (1970), 209-214. Google Scholar

[4] 4. Horvath, J., Topological Vector Spaces and Distributions, Addison-Wesley, Reading, Mass., 1966. Google Scholar

[5] 5. Kiang, M.T., Fixed point theorems for certain classes of semigroups of mappings, Trans. Amer. Math. Soc, 189 (1974), 63-76. Google Scholar

[6] 6. Tan, K.K., Common fixed point theorems for almost weakly periodic nonexpansive mappings, Proc. Amer. Math. Soc. 33 (1972), 355-360. Google Scholar

[7] 7. Tan, K.K., Fixed point theorems for nonexpansive mappings, Pacific Math. J., 41 (1972), 829-842. Google Scholar

[8] 8. Tan, K.K., Some fixed point theorems for nonexpansive mappings in Hausdorff locally convex spaces, Ph.D. Thesis, University of British Columbia, 1970. Google Scholar

[9] 9. Taylor, A.E., Introduction to Functional Analysis, Wiley, New York, 1958. Google Scholar

[10] 10. Kubicek, John D., Applications of Metrics over Tikonov semifields and fixed points in Hilbert spaces, Ph.D. Thesis, University of Missouri-Rolla, 1975. Google Scholar

Cité par Sources :