Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T05:22:10.940Z Has data issue: false hasContentIssue false
  • English
  • Français

Fixed Point Principles for Cones of a Banach Space for the Multivalued Maps Differentiable at the Origin and Infinity

Published online by Cambridge University Press:  20 November 2018

Donald Violette  and
Gilles Fournier
Donald Violette
Affiliation:
Department de mathématiques, Université de Moncton, Monton, New Brunswick
Gilles Fournier
Affiliation:
Department de mathématiques, Université de Moncton, Monton, New Brunswick
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.

In [6] and [7], Krasnosel'skiĭ proved several fundamental fixed point principles for operators leaving invariant a cone in a Banach space. In [9], Nussbaum extended one of the results, the theorem about compression and expansion of a cone, to k-setcontraction maps, k < 1. Other versions for completely continuous maps were given by Fournier-Peitgen [2] and G. Fournier [1].

The purpose of this paper is to generalise some of these results to upper semi continuous multivalued maps which are K-set contractions, k < 1, and differentiable at the origin and infinity.

Keywords

47H0954C6054H25Fixed pointnonexpansive mappinginvariant meannonlinear ergodic theorem
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 4 , 01 August 1992 , pp. 888 - 896
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Fournier, G., Fixed point principles for cones of a linear normed space, Canad. J. Math. (6) XXXII(1980), 1372–1381.Google Scholar
2. Fournier, G. and Peitgen, H.-O., On some fixed point principles for cones in linear normed spaces, Math. Ann. 225 (1977), 205–218.Google Scholar
3. Fournier, G. and Violette, D., A fixed point index for composition of acyclic multivalued maps in Banach spaces, the Mathematical Sciences Research Institute (MSRI)—Korea Publications 1, Operator Equations and Fixed Point Theorems, (1986), 139–158.Google Scholar
4. Fournier, G. and Violette, D., A fixed point theorem for a class of multivalued continuously differentiable maps, Annales Polonici Matematici 47 (1987), 381–402.Google Scholar
5. Fournier, G. and Violette, D., La formule de Leray-Schauderpour l'indice d'une fonction multivoque continûment différentiable, Annales des sciences mathématiques du Québec (15) 1 (1991), 35–53.Google Scholar
6. Krasnosel'skiĭ, M.A., Fixed points of cone-compressing or cone-extending operators, Soviet Math. Dolk. (1960), 1285–1288.Google Scholar
7. Krasnosel'skiĭ, M.A., Positive solutions of operator equations, Groningen, Noordhoff, 1964.Google Scholar
8. Martelli, M., Positive eigenvectors of wedge maps, Annali di Matematica Pura e Applicata (4) 145 (1986), 1–32.Google Scholar
9. Nussbaum, R.D., Periodic solutions of some non-linear autonomous functional differential equations II, J. Diff. Eq. 14 (1973), 360–394.Google Scholar
10. Siegberg, H.W. andSkordev, G., Fixed point index and chain approximations, Pac. J. of Math. (2) 102 (1982), 455–486.Google Scholar