Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-13T16:17:16.687Z Has data issue: false hasContentIssue false

A fixed point theorem in H-space and related results

Published online by Cambridge University Press:  17 April 2009

E. Tarafdar
Affiliation:
Department of Mathematics, The University of Queensland, Queensland 4072, Australia
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.

The equivalence of a fixed point theorem and the Fan-Knaster-Kuratowski-Mazurkiewicz theorem in H-space has been established. The fixed point theorem is then applied to obtain a theorem on sets with H-convex sections, and also results on minimax inequalities.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Allen, G., ‘Variational inequalities, complementary problems and duality theorems’, J. Math. Anal. Appl. 58 (1977), 110.CrossRefGoogle Scholar
[2]Bardaro, C. and Ceppitelli, R., ‘Some further generalizations of Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities’, J. Math. Anal. Appl. 132 (1988), 484490.CrossRefGoogle Scholar
[3]Browder, F.E., ‘Fixed point theory of multivalued mappings in topological vector spaces’, Math. Ann. 177 (1968), 283301.Google Scholar
[4]Fan, K., ‘Some properties of convex sets related to fixed point theorems’, Math. Ann. 266 (1984), 519537.Google Scholar
[5]Fremlin, D.H., Topological Riesz spaces and Measure Theory (Cambridge Univ. Press, London, 1974).CrossRefGoogle Scholar
[6]Horvath, C., ‘Point fixes et coincidences dans les espaces topologiques compacts contractiles’, C.R. Acad. Sci. Paris 299 (1984), 519521.Google Scholar
[7]Horvath, C., ‘Some results on multivalued mappings and inequalities without convexity’, in Nonlinear and Convex Analysis, (Eds. Lin, B.L. and Simons, S.), pp. 99106 (Marcel Dekker, 1989).Google Scholar
[8]Tarafdar, E., ‘A fixed point theorem equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz theorem’, J. Math. Anal. Appl. 128 (1987), 475479.CrossRefGoogle Scholar
[9]Tarafdar, E., ‘A theorem concerning sets with convex sections’, Indian J. Math. 31 (1989), 225228.Google Scholar
[10]Tarafdar, E., ‘Variational problems via a fixed point theorem’, Indian J. Math. 28 (1986), 229240.Google Scholar
[11]Tarafdar, E. and Husain, T., ‘Duality in fixed point theory of multivalued mappings with applications’, J. Math. Anal. Appl. 63 (1978), 371376.Google Scholar