Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T09:29:15.225Z Has data issue: false hasContentIssue false
  • English
  • Français

ORBITALLY NONEXPANSIVE MAPPINGS

Part of: Smooth dynamical systems: general theory Nonlinear operators and their properties

Published online by Cambridge University Press:  11 November 2015

ENRIQUE LLORENS-FUSTER
ENRIQUE LLORENS-FUSTER*
Affiliation:
Department of Mathematical Analysis, University of Valencia, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain email Enrique.Llorens@uv.es
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 define a class of nonlinear mappings which is properly larger than the class of nonexpansive mappings. We also give a fixed point theorem for this new class of mappings.

Keywords

fixed pointnonexpansive mappingnormal structure

MSC classification

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
Secondary: 37C25: Fixed points, periodic points, fixed-point index theory 47H10: Fixed-point theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 3 , June 2016 , pp. 497 - 503
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© 2015 Australian Mathematical Publishing Association Inc.

References

Aoyama, K. and Kohsaka, F., ‘Fixed point theorem for 𝛼-nonexpansive mappings in Banach spaces’, Nonlinear Anal. 74 (2011), 4387–4391.CrossRefGoogle Scholar
Baillon, J. B. and Schoneberg, R., ‘Asymptotic normal structure and fixed points of nonexpansive mappings’, Proc. Amer. Math. Soc. 81 (1981), 257–264.CrossRefGoogle Scholar
Bogin, J., ‘A generalization of a fixed point theorem of Goebel, Kirk and Shimi’, Canad. Math. Bull. 19 (1976), 7–12.Google Scholar
Dhompongsa, S. and Nanan, N., ‘Fixed point theorems by ways of ultra-asymptotic centers’, Abstr. Appl. Anal. 2011 (2011), Article ID 826851, 21 pages, doi:10.1155/2011/826851.CrossRefGoogle Scholar
Díaz, J. B. and Metcalf, F. T., ‘On the structure of the set of subsequential limit points of successive approximations’, Bull. Amer. Math. Soc. 73 (1967), 516–519.Google Scholar
García-Falset, J., Llorens-Fuster, E. and Suzuki, T., ‘Fixed point theory for a class of generalized nonexpansive mappings’, J. Math. Anal. Appl. 375 (2011), 185–195.Google Scholar
Goebel, K. and Kirk, W. A., ‘A fixed point theorem for asymptotically nonexpansive mappings’, Proc. Amer. Math. Soc. 35 (1972), 171–174.Google Scholar
Goebel, K., Kirk, W. A. and Shimi, T. N., ‘A fixed point theorem in uniformly convex spaces’, Boll. Unione Mat. Ital. (9) 7(4) (1973), 67–75.Google Scholar
Kirk, W. A., ‘A fixed point theorem for mappings which do not increase distance’, Amer. Math. Monthly 72 (1965), 1004–1006.CrossRefGoogle Scholar
Llorens-Fuster, E. and Moreno-Gálvez, E., ‘The fixed point theory for some generalized nonexpansive mappings’, Abstr. Appl. Anal. 2011 (2011), Article ID 435686, 15 pages, doi:10.1155/2011/435686.Google Scholar
Suzuki, T., ‘Fixed point theorems and convergence theorems for some generalized nonexpansive mappings’, J. Math. Anal. Appl. 340 (2008), 1088–1095.CrossRefGoogle Scholar