Iterated nonexpansive mappings in Hilbert spaces

Bozena Piatek

doi:10.1007/s11784-021-00898-6

Iterated nonexpansive mappings in Hilbert spaces

Bozena Piatek

Department of Mathematics (RMS/RMS1)

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In [T. Dominguez Benavides and E. Llorens-Fuster, Iterated nonexpansive mappings, J. Fixed Point Theory Appl. 20 (2018), no. 3, Paper No. 104, 18 pp.], the authors raised the question about the existence of a fixed point free continuous INEA mapping T defined on a closed convex and bounded subset (or on a weakly compact convex subset) of a Banach space with normal structure. Our main goal is to give the affirmative answer to this problem in the very special case of a Hilbert space.

Original language	English
Article number	61
Journal	Journal of Fixed Point Theory and Applications
Volume	23
Issue number	4
DOIs	https://doi.org/10.1007/s11784-021-00898-6
Publication status	Published - Nov 2021

Keywords

Hilbert space
asymptotically regular mapping
generalized nonexpansive mapping

ASJC Scopus subject areas

Modeling and Simulation
Geometry and Topology
Applied Mathematics

Access to Document

10.1007/s11784-021-00898-6

Cite this

@article{abc346dbf487441cad95d5c727482575,

title = "Iterated nonexpansive mappings in Hilbert spaces",

abstract = "In [T. Dominguez Benavides and E. Llorens-Fuster, Iterated nonexpansive mappings, J. Fixed Point Theory Appl. 20 (2018), no. 3, Paper No. 104, 18 pp.], the authors raised the question about the existence of a fixed point free continuous INEA mapping T defined on a closed convex and bounded subset (or on a weakly compact convex subset) of a Banach space with normal structure. Our main goal is to give the affirmative answer to this problem in the very special case of a Hilbert space.",

keywords = "Hilbert space, asymptotically regular mapping, generalized nonexpansive mapping",

author = "Bozena Piatek",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s).",

year = "2021",

month = nov,

doi = "10.1007/s11784-021-00898-6",

language = "English",

volume = "23",

journal = "Journal of Fixed Point Theory and Applications",

issn = "1661-7738",

publisher = "Springer International Publishing",

number = "4",

}

TY - JOUR

T1 - Iterated nonexpansive mappings in Hilbert spaces

AU - Piatek, Bozena

PY - 2021/11

Y1 - 2021/11

N2 - In [T. Dominguez Benavides and E. Llorens-Fuster, Iterated nonexpansive mappings, J. Fixed Point Theory Appl. 20 (2018), no. 3, Paper No. 104, 18 pp.], the authors raised the question about the existence of a fixed point free continuous INEA mapping T defined on a closed convex and bounded subset (or on a weakly compact convex subset) of a Banach space with normal structure. Our main goal is to give the affirmative answer to this problem in the very special case of a Hilbert space.

AB - In [T. Dominguez Benavides and E. Llorens-Fuster, Iterated nonexpansive mappings, J. Fixed Point Theory Appl. 20 (2018), no. 3, Paper No. 104, 18 pp.], the authors raised the question about the existence of a fixed point free continuous INEA mapping T defined on a closed convex and bounded subset (or on a weakly compact convex subset) of a Banach space with normal structure. Our main goal is to give the affirmative answer to this problem in the very special case of a Hilbert space.

KW - Hilbert space

KW - asymptotically regular mapping

KW - generalized nonexpansive mapping

UR - https://www.scopus.com/pages/publications/85115101874

U2 - 10.1007/s11784-021-00898-6

DO - 10.1007/s11784-021-00898-6

M3 - Article

AN - SCOPUS:85115101874

SN - 1661-7738

VL - 23

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 4

M1 - 61

ER -

Iterated nonexpansive mappings in Hilbert spaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this