Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T09:15:22.736Z Has data issue: false hasContentIssue false
  • English
  • Français

Fixed points of certain involutions in Banach spaces

Part of: Normed linear spaces and Banach spaces; Banach lattices Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

M. S. Khan  and
M. Imdad
M. S. Khan
Affiliation:
Department of Mathematics Aligarh Muslim UniversityAligarh-202001, India
M. Imdad
Affiliation:
Department of Mathematics Aligarh Muslim UniversityAligarh-202001, India
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.

Some results on fixed points of certain involutions in Banach spaces have been obtained, and whence a few coincidence theorems are also derived. These are indeed generalization of previously known results due to Browder, Goebel-Zlotkiewicz and Iséki. Illustrative examples are also given.

Keywords

involutionBanach spaceconvex setfixed pointcoincidence pointmodulus of convexity.

MSC classification

Secondary: 54H25: Fixed-point and coincidence theorems 46B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 2 , October 1984 , pp. 169 - 177
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Browder, F. E., ‘Nonexpansive nonlinear operators in a Banach space’, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041–1044.Google Scholar
[2]Bryant, V. W., ‘A remark on a fixed point theorem for iterated mappings’, Proc. Amer. Math. Monthly 75 (1968), 399–400.Google Scholar
[3]Ĉiriĉ, Lg. B., ‘A generalization of Banach's contraction principle’, Proc. Amer. Math. Soc. 45 (1974), 267–273.Google Scholar
[4]Goebel, K., ‘An elementary proof of the fixed point theorem of Browder and Kirk’, Michigan Math. J. 16 (1969), 381–383.Google Scholar
[5]Goebel, K. and Zlotkiewicz, E., ‘Some fixed point theorems in Banach spaces’, Colloq. Math. 23 (1971), 103–106.Google Scholar
[6]Hardy, G. E. and Rogers, T. D., ‘A generalization of a fixed point theorem of Reich’, Canad. Math. Bull. 16 (1973), 201–206.Google Scholar
[7]Iséki, K., ‘Fixed point theorem in Banach spaces’, Math. Sem. Notes Kobe Univ. 2 (1974), 11–13.Google Scholar
[8]Kirk, W. A., ‘A fixed point theorem for mappings which do not increase distances’, Amer. Math. Monthly 72 (1965), 1004–1006.Google Scholar
[9]Klee, V., ‘Convex bodies and periodic homeomorphism in Hilbert spaces’, Trans. Amer. Math. Soc. 74 (1953), 10–43.Google Scholar
[10]Réich, S., ‘Some results concerning contraction mappings’, Canad. Math. Bull. 14 (1971), 121–124.Google Scholar