INERTIAL PROXIMAL AND CONTRACTION METHODS FOR SOLVING MONOTONE VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS

Jacob Ashiwere Abuchu; Godwin Chidi Ugwunnadi; Ojen Kumar Narain

doi:10.22771/nfaa.2023.28.01.10

INERTIAL PROXIMAL AND CONTRACTION METHODS FOR SOLVING MONOTONE VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS

Jacob Ashiwere Abuchu^*, Godwin Chidi Ugwunnadi, Ojen Kumar Narain

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

Original language	English
Pages (from-to)	175-203
Number of pages	29
Journal	Nonlinear Functional Analysis and Applications
Volume	28
Issue number	1
DOIs	https://doi.org/10.22771/nfaa.2023.28.01.10
Publication status	Published - 2023
Externally published	Yes

Keywords

Monotone variational inclusion problem
inertial iterative method
nonexpansive operator
pseudocontractive operator
resolvent operator
strong convergence

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10.22771/nfaa.2023.28.01.10

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abstract = "In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.",

keywords = "Monotone variational inclusion problem, inertial iterative method, nonexpansive operator, pseudocontractive operator, resolvent operator, strong convergence",

author = "Abuchu, {Jacob Ashiwere} and Ugwunnadi, {Godwin Chidi} and Narain, {Ojen Kumar}",

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year = "2023",

doi = "10.22771/nfaa.2023.28.01.10",

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AU - Abuchu, Jacob Ashiwere

AU - Ugwunnadi, Godwin Chidi

AU - Narain, Ojen Kumar

PY - 2023

Y1 - 2023

N2 - In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

AB - In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

KW - Monotone variational inclusion problem

KW - inertial iterative method

KW - nonexpansive operator

KW - pseudocontractive operator

KW - resolvent operator

KW - strong convergence

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DO - 10.22771/nfaa.2023.28.01.10

M3 - Article

AN - SCOPUS:85149666956

SN - 1229-1595

VL - 28

SP - 175

EP - 203

JO - Nonlinear Functional Analysis and Applications

JF - Nonlinear Functional Analysis and Applications

IS - 1

ER -

INERTIAL PROXIMAL AND CONTRACTION METHODS FOR SOLVING MONOTONE VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS

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Keywords

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