Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces

Pham Thanh Hieu, Nguyen Thi Thu Thuy, Jean Jacques Strodiot

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

The problem of finding a solution of a variational inequality over the set of common fixed points of a nonexpansive semigroup is considered in a real and uniformly convex Banach space without imposing the sequential weak continuity of the normalized duality mapping. Two new explicit iterative methods are introduced based on the steepest-descent method, and conditions are given to obtain their strong convergence. A numerical example is showed to illustrate the convergence analysis of the proposed methods.

langue originaleAnglais
Pages (de - à)467-483
Nombre de pages17
journalBulletin of the Malaysian Mathematical Sciences Society
Volume42
Numéro de publication2
Les DOIs
étatPublié - 15 mars 2019

Empreinte digitale

Normalized Duality Mapping
Nonexpansive Semigroup
Weak Continuity
Uniformly Convex Banach Space
Steepest Descent Method
Explicit Methods
Iteration Method
Common Fixed Point
Strong Convergence
Convergence Analysis
Variational Inequalities
Banach space
Iteration
Numerical Examples

Citer ceci

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Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces. / Hieu, Pham Thanh; Thuy, Nguyen Thi Thu; Strodiot, Jean Jacques.

Dans: Bulletin of the Malaysian Mathematical Sciences Society, Vol 42, Numéro 2, 15.03.2019, p. 467-483.

Résultats de recherche: Contribution à un journal/une revueArticle

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AU - Strodiot, Jean Jacques

PY - 2019/3/15

Y1 - 2019/3/15

N2 - The problem of finding a solution of a variational inequality over the set of common fixed points of a nonexpansive semigroup is considered in a real and uniformly convex Banach space without imposing the sequential weak continuity of the normalized duality mapping. Two new explicit iterative methods are introduced based on the steepest-descent method, and conditions are given to obtain their strong convergence. A numerical example is showed to illustrate the convergence analysis of the proposed methods.

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KW - Accretive mapping

KW - Common fixed point

KW - Explicit method

KW - Nonexpansive semigroup

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JO - Bulletin of the Malaysian Mathematical Sciences Society

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