Remarks on "some fixed point theorems for s-convex subsets in p-normed spaces"

被引:2
作者
Yu, Lu [1 ]
机构
[1] Univ Paris 1 Pantheon Sorbonne, Ctr Econ Sorbonne, UMR 8074, Paris, France
关键词
Fixed point; Schauder's conjecture; Extreme point; Convex analysis;
D O I
10.1007/s41478-023-00678-0
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We explain why a recent proof of Schauder's conjecture is not correct. A counterexample to a cited intermediate lemma is given.
引用
收藏
页码:1139 / 1143
页数:5
相关论文
共 13 条
[1]  
BESSAGA C, 1975, SELECTED TOPICS INFI
[2]  
Cauty R., 2005, SERDICA MATH J, V31, P309
[3]   A Lefschetz-Hopf theorem for the functions of compact iterations [J].
Cauty, Robert .
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2017, 729 :1-27
[4]  
Cauty R, 2007, J FIX POINT THEORY A, V1, P123, DOI 10.1007/s11784-006-0002-5
[5]   On the conjecture of Schauder [J].
Ennassik, Mohamed ;
Taoudi, Mohamed Aziz .
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2021, 23 (04)
[6]  
Mauldin RD., 1981, SPRINGER, DOI [10.1007/978-3-319-22897-6, DOI 10.1007/978-3-319-22897-6]
[7]   EVERY NEEDLE POINT SPACE CONTAINS A COMPACT CONVEX AR-SET WITH NO EXTREME-POINTS [J].
NHU, NT ;
TRI, LH .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 120 (04) :1261-1265
[8]   NO ROBERTS SPACE IS A COUNTEREXAMPLE TO SCHAUDERS CONJECTURE [J].
NHU, NT ;
TRI, LH .
TOPOLOGY, 1994, 33 (02) :371-378
[9]  
Roberts J.W., 1976, Pathological Compact Convex Sets in Lp(0,1), 0 p andlt
[10]  
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