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

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
Journal	Vietnam Journal of Mathematics
DOIs	https://doi.org/10.1007/s10013-024-00710-1
Publication status	Accepted/In press - 2024
Externally published	Yes

Keywords

47J25
65J15
65K15
90C33
Demimetric mappings
Fixed point problem
Lipschitz continuous mapping
Maximal monotone operator
Monotone inclusion problem

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1007/s10013-024-00710-1

Cite this

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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 = "47J25, 65J15, 65K15, 90C33, 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 = "2024",

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

language = "English",

journal = "Vietnam Journal of Mathematics",

issn = "2305-221X",

publisher = "Springer Science + Business Media",

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TY - JOUR

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 - 2024

Y1 - 2024

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 - 47J25

KW - 65J15

KW - 65K15

KW - 90C33

KW - Demimetric mappings

KW - Fixed point problem

KW - Lipschitz continuous mapping

KW - Maximal monotone operator

KW - Monotone inclusion problem

UR - http://www.scopus.com/inward/record.url?scp=85207892173&partnerID=8YFLogxK

U2 - 10.1007/s10013-024-00710-1

DO - 10.1007/s10013-024-00710-1

M3 - Article

AN - SCOPUS:85207892173

SN - 2305-221X

JO - Vietnam Journal of Mathematics

JF - Vietnam Journal of Mathematics

ER -

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

Abstract

Keywords

UN SDGs

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