The fixed point property and unbounded sets in CAT(0) spaces

Rafa Espínola; Bozena Pia̧tek

doi:10.1016/j.jmaa.2013.06.038

The fixed point property and unbounded sets in CAT(0) spaces

Rafa Espínola
, Bozena Pia̧tek

Katedra Matematyki (RMS/RMS1)

University of Seville

Wyniki badań: Wkład do czasopisma › Artykuł › recenzja

22 Cytowania z bazy Scopus

Abstrakt

In this work we study the fixed point property for nonexpansive self-mappings defined on convex and closed subsets of a CAT(0) space. We will show that a positive answer to this problem is very much linked with the Euclidean geometry of the space while the answer is more likely to be negative if the space is more hyperbolic. As a consequence we extend a very well known result of W.O. Ray on Hilbert spaces.

Język oryginału	angielski
Strony (od–do)	638-654
Liczba stron	17
Czasopismo	Journal of Mathematical Analysis and Applications
Tom	408
Numer wydania	2
Identyfikatory DOI	https://doi.org/10.1016/j.jmaa.2013.06.038
Status publikacji	Opublikowano - 15 gru 2013

Obszary tematyczne ASJC Scopus

Analiza
Matematyka stosowana

Uzyskaj dostęp do dokumentu

10.1016/j.jmaa.2013.06.038

Inne pliki i linki

Link do publikacji w Scopus

Cytuj to

@article{f9dc3d10ab2a413e93a8b8e9678f31db,

title = "The fixed point property and unbounded sets in CAT(0) spaces",

abstract = "In this work we study the fixed point property for nonexpansive self-mappings defined on convex and closed subsets of a CAT(0) space. We will show that a positive answer to this problem is very much linked with the Euclidean geometry of the space while the answer is more likely to be negative if the space is more hyperbolic. As a consequence we extend a very well known result of W.O. Ray on Hilbert spaces.",

keywords = "Banach-Steinhaus theorem, CAT(0) spaces, Fixed points, Nonexpansive mappings, Unbounded convex sets",

author = "Rafa Esp{\'i}nola and Bozena Pi{\c a}tek",

year = "2013",

month = dec,

day = "15",

doi = "10.1016/j.jmaa.2013.06.038",

language = "English",

volume = "408",

pages = "638--654",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - The fixed point property and unbounded sets in CAT(0) spaces

AU - Espínola, Rafa

AU - Pia̧tek, Bozena

PY - 2013/12/15

Y1 - 2013/12/15

N2 - In this work we study the fixed point property for nonexpansive self-mappings defined on convex and closed subsets of a CAT(0) space. We will show that a positive answer to this problem is very much linked with the Euclidean geometry of the space while the answer is more likely to be negative if the space is more hyperbolic. As a consequence we extend a very well known result of W.O. Ray on Hilbert spaces.

AB - In this work we study the fixed point property for nonexpansive self-mappings defined on convex and closed subsets of a CAT(0) space. We will show that a positive answer to this problem is very much linked with the Euclidean geometry of the space while the answer is more likely to be negative if the space is more hyperbolic. As a consequence we extend a very well known result of W.O. Ray on Hilbert spaces.

KW - Banach-Steinhaus theorem

KW - CAT(0) spaces

KW - Fixed points

KW - Nonexpansive mappings

KW - Unbounded convex sets

UR - https://www.scopus.com/pages/publications/84881372772

U2 - 10.1016/j.jmaa.2013.06.038

DO - 10.1016/j.jmaa.2013.06.038

M3 - Article

AN - SCOPUS:84881372772

SN - 0022-247X

VL - 408

SP - 638

EP - 654

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

The fixed point property and unbounded sets in CAT(0) spaces

Abstrakt

Obszary tematyczne ASJC Scopus

Uzyskaj dostęp do dokumentu

Inne pliki i linki

Fingerprint

Cytuj to