APPROXIMATION OF ZEROS OF SUM OF MONOTONE MAPPINGS WITH APPLICATIONS TO VARIATIONAL INEQUALITY AND IMAGE RESTORATION PROBLEMS

Abubakar Adamu; Jitsupa Deepho; Abdulkarim Hassan Ibrahim; Auwal Bala Abubakar

doi:10.22771/nfaa.2021.26.02.12

APPROXIMATION OF ZEROS OF SUM OF MONOTONE MAPPINGS WITH APPLICATIONS TO VARIATIONAL INEQUALITY AND IMAGE RESTORATION PROBLEMS

Abubakar Adamu, Jitsupa Deepho^*, Abdulkarim Hassan Ibrahim, Auwal Bala Abubakar

^*Corresponding author for this work

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

24 Scopus citations

Abstract

In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.

Original language	English
Pages (from-to)	411-432
Number of pages	22
Journal	Nonlinear Functional Analysis and Applications
Volume	26
Issue number	2
DOIs	https://doi.org/10.22771/nfaa.2021.26.02.12
State	Published - 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021. Kyungnam University Press. All Rights Reserved.

Keywords

Monotone
fixed point
image restoration
nonexpansive

ASJC Scopus subject areas

Analysis
Numerical Analysis
Control and Optimization
Applied Mathematics

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10.22771/nfaa.2021.26.02.12

Cite this

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title = "APPROXIMATION OF ZEROS OF SUM OF MONOTONE MAPPINGS WITH APPLICATIONS TO VARIATIONAL INEQUALITY AND IMAGE RESTORATION PROBLEMS",

abstract = "In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.",

keywords = "Monotone, fixed point, image restoration, nonexpansive",

author = "Abubakar Adamu and Jitsupa Deepho and Ibrahim, \{Abdulkarim Hassan\} and Abubakar, \{Auwal Bala\}",

year = "2021",

doi = "10.22771/nfaa.2021.26.02.12",

language = "English",

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AU - Adamu, Abubakar

AU - Deepho, Jitsupa

AU - Ibrahim, Abdulkarim Hassan

AU - Abubakar, Auwal Bala

PY - 2021

Y1 - 2021

N2 - In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.

AB - In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.

KW - Monotone

KW - fixed point

KW - image restoration

KW - nonexpansive

UR - https://www.scopus.com/pages/publications/85107653391

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DO - 10.22771/nfaa.2021.26.02.12

M3 - Article

AN - SCOPUS:85107653391

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VL - 26

SP - 411

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JO - Nonlinear Functional Analysis and Applications

JF - Nonlinear Functional Analysis and Applications

IS - 2

ER -

APPROXIMATION OF ZEROS OF SUM OF MONOTONE MAPPINGS WITH APPLICATIONS TO VARIATIONAL INEQUALITY AND IMAGE RESTORATION PROBLEMS

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this