---
_id: '9315'
abstract:
- lang: eng
  text: We consider inertial iteration methods for Fermat–Weber location problem and
    primal–dual three-operator splitting in real Hilbert spaces. To do these, we first
    obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of
    the inertial Krasnoselskii–Mann iteration for fixed point of nonexpansive operators
    in infinite dimensional real Hilbert spaces under some seemingly easy to implement
    conditions on the iterative parameters. One of our contributions is that the convergence
    analysis and rate of convergence results are obtained using conditions which appear
    not complicated and restrictive as assumed in other previous related results in
    the literature. We then show that Fermat–Weber location problem and primal–dual
    three-operator splitting are special cases of fixed point problem of nonexpansive
    mapping and consequently obtain the convergence analysis of inertial iteration
    methods for Fermat–Weber location problem and primal–dual three-operator splitting
    in real Hilbert spaces. Some numerical implementations are drawn from primal–dual
    three-operator splitting to support the theoretical analysis.
acknowledgement: The research of this author is supported by the Postdoctoral Fellowship
  from Institute of Science and Technology (IST), Austria.
article_number: '75'
article_processing_charge: No
article_type: original
author:
- first_name: Olaniyi S.
  full_name: Iyiola, Olaniyi S.
  last_name: Iyiola
- first_name: Yekini
  full_name: Shehu, Yekini
  id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87
  last_name: Shehu
  orcid: 0000-0001-9224-7139
citation:
  ama: Iyiola OS, Shehu Y. New convergence results for inertial Krasnoselskii–Mann
    iterations in Hilbert spaces with applications. <i>Results in Mathematics</i>.
    2021;76(2). doi:<a href="https://doi.org/10.1007/s00025-021-01381-x">10.1007/s00025-021-01381-x</a>
  apa: Iyiola, O. S., &#38; Shehu, Y. (2021). New convergence results for inertial
    Krasnoselskii–Mann iterations in Hilbert spaces with applications. <i>Results
    in Mathematics</i>. Springer Nature. <a href="https://doi.org/10.1007/s00025-021-01381-x">https://doi.org/10.1007/s00025-021-01381-x</a>
  chicago: Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial
    Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” <i>Results
    in Mathematics</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s00025-021-01381-x">https://doi.org/10.1007/s00025-021-01381-x</a>.
  ieee: O. S. Iyiola and Y. Shehu, “New convergence results for inertial Krasnoselskii–Mann
    iterations in Hilbert spaces with applications,” <i>Results in Mathematics</i>,
    vol. 76, no. 2. Springer Nature, 2021.
  ista: Iyiola OS, Shehu Y. 2021. New convergence results for inertial Krasnoselskii–Mann
    iterations in Hilbert spaces with applications. Results in Mathematics. 76(2),
    75.
  mla: Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial
    Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” <i>Results
    in Mathematics</i>, vol. 76, no. 2, 75, Springer Nature, 2021, doi:<a href="https://doi.org/10.1007/s00025-021-01381-x">10.1007/s00025-021-01381-x</a>.
  short: O.S. Iyiola, Y. Shehu, Results in Mathematics 76 (2021).
date_created: 2021-04-11T22:01:14Z
date_published: 2021-03-25T00:00:00Z
date_updated: 2023-10-10T09:47:33Z
day: '25'
department:
- _id: VlKo
doi: 10.1007/s00025-021-01381-x
external_id:
  isi:
  - '000632917700001'
intvolume: '        76'
isi: 1
issue: '2'
language:
- iso: eng
month: '03'
oa_version: None
publication: Results in Mathematics
publication_identifier:
  eissn:
  - 1420-9012
  issn:
  - 1422-6383
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert
  spaces with applications
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 76
year: '2021'
...
---
_id: '6596'
abstract:
- lang: eng
  text: It is well known that many problems in image recovery, signal processing,
    and machine learning can be modeled as finding zeros of the sum of maximal monotone
    and Lipschitz continuous monotone operators. Many papers have studied forward-backward
    splitting methods for finding zeros of the sum of two monotone operators in Hilbert
    spaces. Most of the proposed splitting methods in the literature have been proposed
    for the sum of maximal monotone and inverse-strongly monotone operators in Hilbert
    spaces. In this paper, we consider splitting methods for finding zeros of the
    sum of maximal monotone operators and Lipschitz continuous monotone operators
    in Banach spaces. We obtain weak and strong convergence results for the zeros
    of the sum of maximal monotone and Lipschitz continuous monotone operators in
    Banach spaces. Many already studied problems in the literature can be considered
    as special cases of this paper.
article_number: '138'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Yekini
  full_name: Shehu, Yekini
  id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87
  last_name: Shehu
  orcid: 0000-0001-9224-7139
citation:
  ama: Shehu Y. Convergence results of forward-backward algorithms for sum of monotone
    operators in Banach spaces. <i>Results in Mathematics</i>. 2019;74(4). doi:<a
    href="https://doi.org/10.1007/s00025-019-1061-4">10.1007/s00025-019-1061-4</a>
  apa: Shehu, Y. (2019). Convergence results of forward-backward algorithms for sum
    of monotone operators in Banach spaces. <i>Results in Mathematics</i>. Springer.
    <a href="https://doi.org/10.1007/s00025-019-1061-4">https://doi.org/10.1007/s00025-019-1061-4</a>
  chicago: Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for
    Sum of Monotone Operators in Banach Spaces.” <i>Results in Mathematics</i>. Springer,
    2019. <a href="https://doi.org/10.1007/s00025-019-1061-4">https://doi.org/10.1007/s00025-019-1061-4</a>.
  ieee: Y. Shehu, “Convergence results of forward-backward algorithms for sum of monotone
    operators in Banach spaces,” <i>Results in Mathematics</i>, vol. 74, no. 4. Springer,
    2019.
  ista: Shehu Y. 2019. Convergence results of forward-backward algorithms for sum
    of monotone operators in Banach spaces. Results in Mathematics. 74(4), 138.
  mla: Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum
    of Monotone Operators in Banach Spaces.” <i>Results in Mathematics</i>, vol. 74,
    no. 4, 138, Springer, 2019, doi:<a href="https://doi.org/10.1007/s00025-019-1061-4">10.1007/s00025-019-1061-4</a>.
  short: Y. Shehu, Results in Mathematics 74 (2019).
date_created: 2019-06-29T10:11:30Z
date_published: 2019-12-01T00:00:00Z
date_updated: 2023-08-28T12:26:22Z
day: '01'
ddc:
- '000'
department:
- _id: VlKo
doi: 10.1007/s00025-019-1061-4
ec_funded: 1
external_id:
  arxiv:
  - '2101.09068'
  isi:
  - '000473237500002'
file:
- access_level: open_access
  checksum: c6d18cb1e16fc0c36a0e0f30b4ebbc2d
  content_type: application/pdf
  creator: kschuh
  date_created: 2019-07-03T15:20:40Z
  date_updated: 2020-07-14T12:47:34Z
  file_id: '6605'
  file_name: Springer_2019_Shehu.pdf
  file_size: 466942
  relation: main_file
file_date_updated: 2020-07-14T12:47:34Z
has_accepted_license: '1'
intvolume: '        74'
isi: 1
issue: '4'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '12'
oa: 1
oa_version: Published Version
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '616160'
  name: 'Discrete Optimization in Computer Vision: Theory and Practice'
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Results in Mathematics
publication_identifier:
  eissn:
  - 1420-9012
  issn:
  - 1422-6383
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence results of forward-backward algorithms for sum of monotone operators
  in Banach spaces
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 74
year: '2019'
...