Inertial Halpern-type method for solving monotone variational inequality and fixed point problems in Banach spaces

Ikechukwu G. Ezugorie; Lawal Y. Haruna; Godwin C. Ugwunnadi; Eric U. Ofoedu

doi:10.15446/recolma.v58n2.121038

Inertial Halpern-type method for solving monotone variational inequality and fixed point problems in Banach spaces

Ikechukwu G. Ezugorie
, Lawal Y. Haruna
, Godwin C. Ugwunnadi^*
, Eric U. Ofoedu

^*Corresponding author for this work

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

Abstract

In this paper, we introduce inertial Tseng’s method and Halpern-type algorithm for solving monotone variational inequality and fixed point problems in 2-uniformly convex and 2-uniformly smooth real Banach spaces. We establish strong convergence of our proposed method under some assumptions on parameters without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of our main result.

Original language	English
Pages (from-to)	165-189
Number of pages	25
Journal	Revista Colombiana de Matematicas
Volume	58
Issue number	2
DOIs	https://doi.org/10.15446/recolma.v58n2.121038
Publication status	Published - 19 Jun 2025
Externally published	Yes

Keywords

Banach space
Halpern Tseng’s extradient subgradient method
Inertial method
Strong convergence
demigeneralized mapping
monotone variational inequality problem

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10.15446/recolma.v58n2.121038

Cite this

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title = "Inertial Halpern-type method for solving monotone variational inequality and fixed point problems in Banach spaces",

abstract = "In this paper, we introduce inertial Tseng{\textquoteright}s method and Halpern-type algorithm for solving monotone variational inequality and fixed point problems in 2-uniformly convex and 2-uniformly smooth real Banach spaces. We establish strong convergence of our proposed method under some assumptions on parameters without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of our main result.",

keywords = "Banach space, Halpern Tseng{\textquoteright}s extradient subgradient method, Inertial method, Strong convergence, demigeneralized mapping, monotone variational inequality problem",

author = "Ezugorie, \{Ikechukwu G.\} and Haruna, \{Lawal Y.\} and Ugwunnadi, \{Godwin C.\} and Ofoedu, \{Eric U.\}",

year = "2025",

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doi = "10.15446/recolma.v58n2.121038",

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AU - Ezugorie, Ikechukwu G.

AU - Haruna, Lawal Y.

AU - Ugwunnadi, Godwin C.

AU - Ofoedu, Eric U.

PY - 2025/6/19

Y1 - 2025/6/19

N2 - In this paper, we introduce inertial Tseng’s method and Halpern-type algorithm for solving monotone variational inequality and fixed point problems in 2-uniformly convex and 2-uniformly smooth real Banach spaces. We establish strong convergence of our proposed method under some assumptions on parameters without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of our main result.

AB - In this paper, we introduce inertial Tseng’s method and Halpern-type algorithm for solving monotone variational inequality and fixed point problems in 2-uniformly convex and 2-uniformly smooth real Banach spaces. We establish strong convergence of our proposed method under some assumptions on parameters without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of our main result.

KW - Banach space

KW - Halpern Tseng’s extradient subgradient method

KW - Inertial method

KW - Strong convergence

KW - demigeneralized mapping

KW - monotone variational inequality problem

UR - https://www.scopus.com/pages/publications/105029113663

U2 - 10.15446/recolma.v58n2.121038

DO - 10.15446/recolma.v58n2.121038

M3 - Article

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SP - 165

EP - 189

JO - Revista Colombiana de Matematicas

JF - Revista Colombiana de Matematicas

IS - 2

ER -

Inertial Halpern-type method for solving monotone variational inequality and fixed point problems in Banach spaces

Abstract

Keywords

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