Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-19T11:51:06.217Z Has data issue: false hasContentIssue false

Perturbation theory of multivalued atkinson operators in normed spaces

Published online by Cambridge University Press:  17 April 2009

Teresa Álvarez
Affiliation:
Department of Mathematics, University of Oviedo, 33007, OviedoAsturias, Spain e-mail: seco@uniovi.es
Diane Wilcox
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7700, South Africa e-mail: diane@maths.uct.ac.za
Rights & Permissions [Opens in a new window]

Extract

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 prove several stability results for Atkinson linear relations under additive perturbation by small norm, strictly singular and strictly cosingular multivalued linear operators satisfying some additional conditions.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Agarwal, R.P., Mehan, M. and O'Regan, D., Fixed point theory and applications (Cambridge University Press, Cambridge, London, 2001).CrossRefGoogle Scholar
[2]Álvarez, T., ‘On almost semi-Fredholm linear relations in normed spaces’, Glasgow Math. J. 47 (2005), 187193.CrossRefGoogle Scholar
[3]Álvarez, T., Cross, R.W. and Wilcox, D., ‘Multivalued Fredholm type operators with abstract generalised inverses’, J. Math. Anal. Appl. 261 (2001), 403417.CrossRefGoogle Scholar
[4]Cross, R.W., Multivalued linear operators (Marcel Dekker, New York, 1998).Google Scholar
[5]Favini, A. and Yagi, A., ‘Multivalued linear operators and degenerate evolution equations’, Ann. Mat. Pura. Appl. (4) 163 (1993), 353384.CrossRefGoogle Scholar
[6]González, M., ‘On Atkinson operators in locally convex spaces’, Math. Z. 190 (1985), 505517.CrossRefGoogle Scholar
[7]Gorniewicz, L., Topological fixed point theory of multivalued mappings (Kluwer, Dordrecht, 1999).CrossRefGoogle Scholar
[8]Gromov, M., Partial differential relations (Springer-Verlag, Berlin, 1966).Google Scholar
[9]Kato, T., ‘Perturbation theory for nullity, deficiency and other quantities of linear operators’, J. Anal. Math. 6 (1958), 261322.CrossRefGoogle Scholar
[10]Müller-Hörrig, V., ‘Zur theorie der semi-Fredolm-operatoren mit stetig projizierten Kern und Bild’, Math. Nach. 99 (1980), 185197.CrossRefGoogle Scholar
[11]Muresan, M., ‘On a boundary value problem for quasi-linear differential inclusions of evolution’, Collect. Math. 45 (1994), 165175.Google Scholar
[12]von Neumann, J., Functorial operators Vol. 2, The Geometry of Orthogonal Spaces Annals of Math. Studies, 22 (Princeton University Press, Princeton N. J., 1950).Google Scholar
[13]Román-Flores, H.A., Flores-Franulic, A., Rojas-Medar, M.A. and Bassanezi, R.C., ‘Stability of the fixed points set of fuzzy contractions’, Appl. Math. Lett. 11 (1998), 3337.CrossRefGoogle Scholar
[14]Vladimirskii, J.I., ‘Strictly cosingular operators’, Soviet Math. Dokl. 8 (1967), 739740.Google Scholar
[15]Yuanguo, Z. and Ling, R., ‘Differential inclusions for fuzzy maps’, Fuzzy sets and Systems 112 (2000).Google Scholar