Browder's Convergence for One-Parameter Nonexpansive Semigroups
Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 15-25

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

We give the sufficient and necessary conditions of Browder's convergence theorem for one-parameter nonexpansive semigroups which was proved by Suzuki. We also discuss the perfect kernels of topological spaces.
DOI : 10.4153/CMB-2011-071-9
Mots-clés : 47H20, nonexpansive semigroup, common fixed point, Browder's convergence, perfect kernel
Akiyama, Shigeki; Suzuki, Tomonari. Browder's Convergence for One-Parameter Nonexpansive Semigroups. Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 15-25. doi: 10.4153/CMB-2011-071-9
@article{10_4153_CMB_2011_071_9,
     author = {Akiyama, Shigeki and Suzuki, Tomonari},
     title = {Browder's {Convergence} for {One-Parameter} {Nonexpansive} {Semigroups}},
     journal = {Canadian mathematical bulletin},
     pages = {15--25},
     year = {2012},
     volume = {55},
     number = {1},
     doi = {10.4153/CMB-2011-071-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-071-9/}
}
TY  - JOUR
AU  - Akiyama, Shigeki
AU  - Suzuki, Tomonari
TI  - Browder's Convergence for One-Parameter Nonexpansive Semigroups
JO  - Canadian mathematical bulletin
PY  - 2012
SP  - 15
EP  - 25
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-071-9/
DO  - 10.4153/CMB-2011-071-9
ID  - 10_4153_CMB_2011_071_9
ER  - 
%0 Journal Article
%A Akiyama, Shigeki
%A Suzuki, Tomonari
%T Browder's Convergence for One-Parameter Nonexpansive Semigroups
%J Canadian mathematical bulletin
%D 2012
%P 15-25
%V 55
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-071-9/
%R 10.4153/CMB-2011-071-9
%F 10_4153_CMB_2011_071_9

[1] [1] Belluce, L. P. and Kirk, W. A., Nonexpansive mappings and fixed-points in Banach spaces. Illinois J. Math 11(1967), 474–479. Google Scholar

[2] [2] Browder, F. E., Nonexpansive nonlinear operators in a Banach space. Proc. Nat. Acad. Sci. U.S.A. 54(1965), 1041–1044. doi:10.1073/pnas.54.4.1041 Google Scholar

[3] [3] Browder, F. E., Convergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces. Arch. Rational Mech. Anal. 24(1967), 82–90. Google Scholar

[4] [4] Bruck, R. E., A common fixed point theorem for a commuting family of nonexpansive mappings. Pacific J. Math. 53(1974), 59–71. Google Scholar

[5] [5] DeMarr, R., Common fixed points for commuting contraction mappings. Pacific J. Math. 13(1963), 1139–1141. Google Scholar

[6] [6] Goebel, K. and Kirk, W. A., Topics in Metric Fixed Point Theory. Cambridge Studies in Advanced Mathematics 28, Cambridge University Press Cambridge, 1990. Google Scholar

[7] [7] Kirk, W. A. and Sims, B., (eds.) Handbook of Metric Fixed Point Theory. Kluwer Academic Publishers, dordrecht, 2001. Google Scholar

[8] [8] Kuratowski, K., Topology. I. Academic Press, New York, 1966. Google Scholar

[9] [9] Lim, T. C., A fixed point theorem for families on nonexpansive mappings. Pacific J. Math. 53(1974), 487–493. Google Scholar

[10] [10] Suzuki, T., On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces. Proc. Amer. Math. Soc. 131(2003), no. 7, 2133–2136. doi:10.1090/S0002-9939-02-06844-2 Google Scholar

[11] [11] Suzuki, T., Common fixed points of one-parameter nonexpansive semigroups. Bull. London Math. Soc. 38(2006), no. 6, 1009–1018. doi:10.1112/S0024609306018893 Google Scholar

[12] [12] Suzuki, T., Browder's type convergence theorems for one-parameter semigroups of nonexpansive mappings in Banach spaces. Israel J. Math. 157(2007), 239–257. doi:10.1007/s11856-006-0010-6 Google Scholar

[13] [13] Suzuki, T., Some comments about recent results on one-parameter nonexpansive semigroups. Bull. Kyushu Inst. Technol. Pure Appl. Math. 54(2007), 13–26. Google Scholar

[14] [14] Suzuki, T., Browder convergence and Mosco convergence for families of nonexpansive mappings. Cubo 10(2008), no. 4, 101–108. Google Scholar

[15] [15] Takahashi, W., Nonlinear Functional Analysis. Fixed Point Theory and its Applications. Yokohama Publishers, Yokohama, 2000. Google Scholar

[16] [16] Willard, S., General Topology. Dover, Mineola, NY, 2004. Google Scholar

Cité par Sources :