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Fixed points of approximable maps


Author: Sehie Park
Journal: Proc. Amer. Math. Soc. 124 (1996), 3109-3114
MSC (1991): Primary 47H10, 54C60; Secondary 54H25, 49J35, 49K35, 52A07, 55M20
DOI: https://doi.org/10.1090/S0002-9939-96-03512-5
MathSciNet review: 1343717
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Abstract: We present a simple proof of the Leray-Schauder type theorem for approximable multimaps given recently by Ben-El-Mechaiekh and Idzik. We apply this theorem to obtain a Schaefer type theorem, the Birkhoff-Kellogg type theorems, a Penot type theorem for non-self-maps, and quasi-variational inequalities, all related to compact closed approximable maps.


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Additional Information

Sehie Park
Affiliation: Department of Mathematics, Seoul National University, Seoul 151–742, Korea
Email: shpark@math.snu.ac.kr

DOI: https://doi.org/10.1090/S0002-9939-96-03512-5
Keywords: Hausdorff topological vector space (t.v.s.), multimap (map), $(U, V)$-approximative continuous selection, approximable, closed map, compact map, theorems of Leray-Schauder type, Schaefer type, Birkhoff-Kellogg type, quasi-variational or variational inequalities
Received by editor(s): March 30, 1995
Additional Notes: Supported in part by KOSEF-951-0102-006-2.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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