Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T05:33:06.139Z Has data issue: false hasContentIssue false
  • English
  • Français

Browder's Convergence for One-Parameter Nonexpansive Semigroups

Published online by Cambridge University Press:  20 November 2018

Shigeki Akiyama  and
Tomonari Suzuki
Shigeki Akiyama
Affiliation:
Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan e-mail: [email protected]
Tomonari Suzuki
Affiliation:
Department of Basic Sciences, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

47H20nonexpansive semigroupcommon fixed pointBrowder's convergenceperfect kernel
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 1 , 01 March 2012 , pp. 15 - 25
Copyright
Copyright © Canadian Mathematical Society 2012

References

[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] 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.54.4.1041Google Scholar
[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] 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] DeMarr, R., Common fixed points for commuting contraction mappings. Pacific J. Math. 13(1963), 1139–1141.Google Scholar
[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] Kirk, W. A. and Sims, B., (eds.) Handbook of Metric Fixed Point Theory. Kluwer Academic Publishers, dordrecht, 2001.Google Scholar
[8] Kuratowski, K., Topology. I. Academic Press, New York, 1966.Google Scholar
[9] Lim, T. C., A fixed point theorem for families on nonexpansive mappings. Pacific J. Math. 53(1974), 487–493.Google Scholar
[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/S0002-9939-02-06844-2Google Scholar
[11] Suzuki, T., Common fixed points of one-parameter nonexpansive semigroups. Bull. London Math. Soc. 38(2006), no. 6, 1009–1018. doi:10.1112/S0024609306018893Google Scholar
[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/s11856-006-0010-6Google Scholar
[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] Suzuki, T., Browder convergence and Mosco convergence for families of nonexpansive mappings. Cubo 10(2008), no. 4, 101–108.Google Scholar
[15] Takahashi, W., Nonlinear Functional Analysis. Fixed Point Theory and its Applications. Yokohama Publishers, Yokohama, 2000.Google Scholar
[16] Willard, S., General Topology. Dover, Mineola, NY, 2004.Google Scholar