A Modified Forward-Backward Splitting Method for Solving Monotone Inclusions and Fixed Points Problems

Abd Semii O.E. Owolabi; Oluwatosin T. Mewomo; Adeolu Taiwo; Lateef O. Jolaoso; Aviv Gibali

doi:10.1007/s10013-024-00710-1

A Modified Forward-Backward Splitting Method for Solving Monotone Inclusions and Fixed Points Problems

Abd Semii O.E. Owolabi
, Oluwatosin T. Mewomo
, Adeolu Taiwo
, Lateef O. Jolaoso
, Aviv Gibali^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

In this work we present a new iterative algorithm for solving monotone inclusion problem and common fixed point problem of a finite family of demimetric mappings in a real Hilbert spaces. We combine several techniques, such as the Armijo line search and inertia to establish a modified forward-backward splitting method for solving the problem. Under standard assumptions we establish the strong convergence of the algorithm and present two numerical examples to illustrate and compare the performances of the method and related ones.

Original language	English
Pages (from-to)	591-612
Number of pages	22
Journal	Vietnam Journal of Mathematics
Volume	53
Issue number	3
DOIs	https://doi.org/10.1007/s10013-024-00710-1
Publication status	Published - Jul 2025
Externally published	Yes

Keywords

Demimetric mappings
Fixed point problem
Lipschitz continuous mapping
Maximal monotone operator
Monotone inclusion problem

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10.1007/s10013-024-00710-1

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@article{52b082f10cf948198627f151f94d162a,

title = "A Modified Forward-Backward Splitting Method for Solving Monotone Inclusions and Fixed Points Problems",

abstract = "In this work we present a new iterative algorithm for solving monotone inclusion problem and common fixed point problem of a finite family of demimetric mappings in a real Hilbert spaces. We combine several techniques, such as the Armijo line search and inertia to establish a modified forward-backward splitting method for solving the problem. Under standard assumptions we establish the strong convergence of the algorithm and present two numerical examples to illustrate and compare the performances of the method and related ones.",

keywords = "Demimetric mappings, Fixed point problem, Lipschitz continuous mapping, Maximal monotone operator, Monotone inclusion problem",

author = "Owolabi, \{Abd Semii O.E.\} and Mewomo, \{Oluwatosin T.\} and Adeolu Taiwo and Jolaoso, \{Lateef O.\} and Aviv Gibali",

note = "Publisher Copyright: {\textcopyright} Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2024.",

year = "2025",

month = jul,

doi = "10.1007/s10013-024-00710-1",

language = "English",

volume = "53",

pages = "591--612",

journal = "Vietnam Journal of Mathematics",

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T1 - A Modified Forward-Backward Splitting Method for Solving Monotone Inclusions and Fixed Points Problems

AU - Owolabi, Abd Semii O.E.

AU - Mewomo, Oluwatosin T.

AU - Taiwo, Adeolu

AU - Jolaoso, Lateef O.

AU - Gibali, Aviv

N1 - Publisher Copyright: © Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2024.

PY - 2025/7

Y1 - 2025/7

N2 - In this work we present a new iterative algorithm for solving monotone inclusion problem and common fixed point problem of a finite family of demimetric mappings in a real Hilbert spaces. We combine several techniques, such as the Armijo line search and inertia to establish a modified forward-backward splitting method for solving the problem. Under standard assumptions we establish the strong convergence of the algorithm and present two numerical examples to illustrate and compare the performances of the method and related ones.

AB - In this work we present a new iterative algorithm for solving monotone inclusion problem and common fixed point problem of a finite family of demimetric mappings in a real Hilbert spaces. We combine several techniques, such as the Armijo line search and inertia to establish a modified forward-backward splitting method for solving the problem. Under standard assumptions we establish the strong convergence of the algorithm and present two numerical examples to illustrate and compare the performances of the method and related ones.

KW - Demimetric mappings

KW - Fixed point problem

KW - Lipschitz continuous mapping

KW - Maximal monotone operator

KW - Monotone inclusion problem

UR - https://www.scopus.com/pages/publications/85207892173

U2 - 10.1007/s10013-024-00710-1

DO - 10.1007/s10013-024-00710-1

M3 - Article

AN - SCOPUS:85207892173

SN - 2305-221X

VL - 53

SP - 591

EP - 612

JO - Vietnam Journal of Mathematics

JF - Vietnam Journal of Mathematics

IS - 3

ER -

A Modified Forward-Backward Splitting Method for Solving Monotone Inclusions and Fixed Points Problems

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Keywords

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