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

页码：275 / 282

页数：8

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

← 1 2 →