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New fixed point theorems for a family of mappings and applications to problems on sets with convex sections

Author(s): Kunquan Lan; Jeffrey Webb
Journal: Proc. Amer. Math. Soc. 126 (1998), 1127-1132.
MSC (1991): Primary 46A55, 47H04, 47H10, 54H25; Secondary 49J40
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Abstract: Some new fixed point theorems for a family of mappings are obtained and applied to problems on sets with convex sections that were first studied by Ky Fan.

References:

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F.E. Browder, The fixed point theory of multi-valued mappings in topological vector spaces, Math.Ann. 177(1968), 283-301. MR 37:4679
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Ky Fan, Sur un théorème minimax, C.R.Acad.Sci. Paris, 259(1964), 3925-3928. MR 30:5145
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Ky Fan, Applications of a theorem concerning sets with convex sections, Math. Ann. 163(1966), 189-203. MR 32:8101
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Ky Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266(1984), 519-537. MR 85i:47060
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Additional Information:

Kunquan Lan
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, United Kingdom
Email: kl@maths.gla.ac.uk

Jeffrey Webb
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, United Kingdom
Email: jrlw@maths.gla.ac.uk

DOI: 10.1090/S0002-9939-98-04347-0
PII: S 0002-9939(98)04347-0
Keywords: Fixed point, partition of unity, sets with convex sections.
Received by editor(s): September 23, 1996
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1998, American Mathematical Society

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