Viscosity method with a ϕ-contraction mapping for hierarchical variational inequalities on hadamard manifolds

Suliman Al-Homidan; Qamrul Hasan Ansari; Feeroz Babu; Jen Chih Yao

doi:10.24193/fpt-ro.2020.2.40

Viscosity method with a ϕ-contraction mapping for hierarchical variational inequalities on hadamard manifolds

Suliman Al-Homidan, Qamrul Hasan Ansari, Feeroz Babu, Jen Chih Yao^*

^*Corresponding author for this work

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

14 Scopus citations

Abstract

In this paper, we propose the viscosity method for solving variational inequality problems defined over a set of fixed points of a nonexpansive mapping and involving a ϕ-contraction mapping and another nonexpansive mapping in the setting of Hadamard manifolds. Several special cases of such a variational inequality problem are also considered. The convergence analysis of the proposed method is studied. We illustrate proposed algorithm and convergence result by a numerical example. The algorithms and convergence results of this paper extend and improve several known algorithms and results from linear structure to Hadamard manifolds.

Original language	English
Pages (from-to)	561-584
Number of pages	24
Journal	Fixed Point Theory
Volume	21
Issue number	2
DOIs	https://doi.org/10.24193/fpt-ro.2020.2.40
State	Published - 2020

Bibliographical note

Publisher Copyright:
© 2020, House of the Book of Science. All rights reserved.

Keywords

Geodesic convexity
Hadamard manifolds
Hierarchical minimization problem
Hierarchical variational inequality problem
Monotone vector fields
Moreau-Yosida regularization
Nonexpansive mappings
Viscosity method
ϕ-contraction mappings

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.24193/fpt-ro.2020.2.40

Cite this

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title = "Viscosity method with a ϕ-contraction mapping for hierarchical variational inequalities on hadamard manifolds",

abstract = "In this paper, we propose the viscosity method for solving variational inequality problems defined over a set of fixed points of a nonexpansive mapping and involving a ϕ-contraction mapping and another nonexpansive mapping in the setting of Hadamard manifolds. Several special cases of such a variational inequality problem are also considered. The convergence analysis of the proposed method is studied. We illustrate proposed algorithm and convergence result by a numerical example. The algorithms and convergence results of this paper extend and improve several known algorithms and results from linear structure to Hadamard manifolds.",

keywords = "Geodesic convexity, Hadamard manifolds, Hierarchical minimization problem, Hierarchical variational inequality problem, Monotone vector fields, Moreau-Yosida regularization, Nonexpansive mappings, Viscosity method, ϕ-contraction mappings",

author = "Suliman Al-Homidan and Ansari, \{Qamrul Hasan\} and Feeroz Babu and Yao, \{Jen Chih\}",

year = "2020",

doi = "10.24193/fpt-ro.2020.2.40",

language = "English",

volume = "21",

pages = "561--584",

journal = "Fixed Point Theory",

issn = "1583-5022",

publisher = "House of the Book of Science",

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TY - JOUR

T1 - Viscosity method with a ϕ-contraction mapping for hierarchical variational inequalities on hadamard manifolds

AU - Al-Homidan, Suliman

AU - Ansari, Qamrul Hasan

AU - Babu, Feeroz

AU - Yao, Jen Chih

PY - 2020

Y1 - 2020

N2 - In this paper, we propose the viscosity method for solving variational inequality problems defined over a set of fixed points of a nonexpansive mapping and involving a ϕ-contraction mapping and another nonexpansive mapping in the setting of Hadamard manifolds. Several special cases of such a variational inequality problem are also considered. The convergence analysis of the proposed method is studied. We illustrate proposed algorithm and convergence result by a numerical example. The algorithms and convergence results of this paper extend and improve several known algorithms and results from linear structure to Hadamard manifolds.

AB - In this paper, we propose the viscosity method for solving variational inequality problems defined over a set of fixed points of a nonexpansive mapping and involving a ϕ-contraction mapping and another nonexpansive mapping in the setting of Hadamard manifolds. Several special cases of such a variational inequality problem are also considered. The convergence analysis of the proposed method is studied. We illustrate proposed algorithm and convergence result by a numerical example. The algorithms and convergence results of this paper extend and improve several known algorithms and results from linear structure to Hadamard manifolds.

KW - Geodesic convexity

KW - Hadamard manifolds

KW - Hierarchical minimization problem

KW - Hierarchical variational inequality problem

KW - Monotone vector fields

KW - Moreau-Yosida regularization

KW - Nonexpansive mappings

KW - Viscosity method

KW - ϕ-contraction mappings

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DO - 10.24193/fpt-ro.2020.2.40

M3 - Article

AN - SCOPUS:85102265554

SN - 1583-5022

VL - 21

SP - 561

EP - 584

JO - Fixed Point Theory

JF - Fixed Point Theory

IS - 2

ER -

Viscosity method with a ϕ-contraction mapping for hierarchical variational inequalities on hadamard manifolds

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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