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Fixed points of approximable maps
Author(s):
Sehie
Park
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3109-3114.
MSC (1991):
Primary 47H10, 54C60;
Secondary 54H25, 49J35, 49K35, 52A07, 55M20
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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.
References:
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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:
10.1090/S0002-9939-96-03512-5
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Lai-Jiu Lin and Zenn-Tsuen Yu, Fixed point theorems of KKM-type maps, Nonlinear Anal. 38 (1999), 265--275. MR 1 697 055
R.P. Agarwal and D. O'Regan, Continuation Methods for Closed, Weakly Closed, DKT, and WDKT Maps, Comput. Math. Appl. 38 (1999), 81--88. MR CMP 1 713 164
R.P. Agarwal and D. O'Regan, Topological Essentiality and Fixed Point Theory, Appl. Math. Lett. 12 (1999), 5--10.
Sehie Park and Kwang Sik Jeong, The Leray-Schauder principles for condensing approximable and other multimaps , Nonlinear Anal. Forum 4 (1999), 157--173. MR 1 736 510
Hichem Ben-El-Mechaiekh, Spaces and maps approximation and fixed points, J. Comput. Appl. Math. 113 (2000), 283--308.
R.P. Agarwal and D. O'Regan, A Note on the Existence of Multiple Fixed Points for Multivalued Maps with Applications, J. Differential Equations 160 (2000), 389--403. MR CMP 1 736 998
R.P. Agarwal and D. O'Regan, Essential and Inessential Maps and Continuation Theorems, Appl. Math. Lett. 13 (2000), 83--90.
R.P. Agarwal and D. O'Regan, Multivalued Essential Maps of Approximable and Acyclic Type, Appl. Math. Lett. 13 (2000), 7--11.
George Xian-Zhi Yuan , KKM theory and applications in nonlinear analysis, Monographs and textbooks in pure and applied mathematics, vol. 218, Marcel Dekker, 1999. MR 2000b:49002
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