Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-14T03:23:16.620Z Has data issue: false hasContentIssue false
  • English
  • Français

FIXED POINT THEORY FOR VARIOUS CLASSES OF INWARD MULTIVALUED MAPS

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  21 October 2009

RAVI P. AGARWAL  and
DONAL O’REGAN
RAVI P. AGARWAL*
Affiliation:
Department of Mathematical Science, Florida Institute of Technology, Melbourne, Florida 32901, USA (email: [email protected])
DONAL O’REGAN
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland (email: [email protected])
*
✉For correspondence; 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.

In this paper we present new fixed point theorems for inward and weakly inward type maps between Fréchet spaces. We also discuss Kakutani–Mönch and contractive type maps.

Keywords

fixed point theoryprojective limits

MSC classification

Secondary: 47H10: Fixed-point theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 1 , February 2010 , pp. 1 - 15
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

References

[1]Agarwal, R. P., Dshalalow, J. and O’Regan, D., ‘Fixed point and homotopy results for generalized contractive maps of Reich type’, Appl. Anal. 82 (2003), 329–350.CrossRefGoogle Scholar
[2]Agarwal, R. P., Dshalalow, J. H. and O’Regan, D., ‘Fixed point theory for Mönch type maps defined on closed subsets of Fréchet spaces: the projective limit approach’, Int. J. Math. Math. Sci. 17 (2005), 2775–2782.CrossRefGoogle Scholar
[3]Agarwal, R. P., Dshalalow, J. H. and O’Regan, D., ‘Leray–Schauder principles for inward Kakutani Mönch type maps’, Nonlinear Funct. Anal. Appl. 10 (2005), 325–330.Google Scholar
[4]Agarwal, R. P., Frigon, M. and O’Regan, D., ‘A survey of recent fixed point theory in Fréchet spaces’, in: Nonlinear Analysis and Applications: to V. Lakshmikantham on his 80th Birthday, Vol. 1 (Kluwer Academic Publishers, Dordrecht, 2003), pp. 75–88.Google Scholar
[5]Agarwal, R. P. and O’Regan, D., ‘Fixed point theory for weakly inward Kakutani maps: the projective limit approach’, Proc. Amer. Math. Soc. 135 (2007), 417–426.CrossRefGoogle Scholar
[6]Deimling, K., Multivalued Differential Equations (Walter de Gruyter, Berlin, 1992).CrossRefGoogle Scholar
[7]Kantorovich, L. V. and Akilov, G. P., Functional Analysis in Normed Spaces (Pergamon Press, Oxford, 1964).Google Scholar
[8]O’Regan, D., ‘Fixed point theorems for nonlinear operators’, J. Math. Anal. Appl. 202 (1996), 413–432.CrossRefGoogle Scholar
[9]O’Regan, D., ‘A continuation theory for weakly inward maps’, Glasg. Math. J. 40 (1998), 311–321.CrossRefGoogle Scholar
[10]O’Regan, D., ‘Homotopy and Leray–Schauder type results for admissible inward multimaps’, J. Concr. Appl. Math. 2 (2004), 67–76.Google Scholar
[11]O’Regan, D., ‘Leray–Schauder results for inward acyclic and approximable maps defined on Fréchet space’, Appl. Math. Lett. 19 (2006), 976–982.CrossRefGoogle Scholar
[12]O’Regan, D., ‘Fixed point theory in Fréchet spaces for Mönch inward and contractive Urysohn type operators’, East Asian Math. J. 24 (2008), 233–249.Google Scholar
[13]O’Regan, D. and Precup, R., ‘Fixed point theory for set valued maps and existence principles for integral inclusions’, J. Math. Anal. Appl. 245 (2000), 594–612.CrossRefGoogle Scholar