A porosity theorem for a class of nonexpansive set-valued mappings

被引:0
作者
Reich, Simeon [1 ]
Zaslavski, Alexander J. [1 ]
机构
[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
来源
COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS VII | 2017年 / 699卷
关键词
Approximate fixed point; complete metric space; fixed point; Hausdorff metric; hyperbolic space; nonexpansive mapping; porosity; set-valued mapping; FIXED-POINTS; ITERATIONS;
D O I
10.1090/conm/699/14096
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a complete metric space (M, d) of nonexpansive set valued self-mappings of a closed and convex (not necessarily bounded) set in a Banach space. We show that the subset of (M, d) which consists of those mappings which have approximate fixed points has a sigma-porous complement in (M, d).
引用
收藏
页码:275 / 282
页数:8
相关论文
共 16 条
[1]  
[Anonymous], 1993, DYNAM SYSTEMS APPL
[2]  
BANACH S., 1922, Fundam. Math., V3, P133, DOI DOI 10.4064/FM-3-1-133-181
[3]  
DeBlasi F.S., 1976, C R ACAD SCI PARIS A, V283, pA185
[4]  
DEBLASI FS, 1989, CR ACAD SCI I-MATH, V308, P51
[5]  
Goebel K., 1990, Cambridge Studies in Advanced Mathematics, V28, P244, DOI [10.1017/CBO9780511526152, DOI 10.1017/CBO9780511526152]
[6]  
Goebel Kazimierz, 1984, MONOGRAPHS TXB PURE, V83
[7]  
Kirk WA, 2001, HANDBOOK OF METRIC FIXED POINT THEORY, P1
[8]  
Rakotch E., 1962, Proc. Amer. Math. Soc., V13, P459
[9]   NONEXPANSIVE ITERATIONS IN HYPERBOLIC SPACES [J].
REICH, S ;
SHAFRIR, I .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 15 (06) :537-558
[10]   Convergence of Krasnoselskii-Mann iterations of nonexpansive operators [J].
Reich, S ;
Zaslavski, AJ .
MATHEMATICAL AND COMPUTER MODELLING, 2000, 32 (11-13) :1423-1431