Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces

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

    Research output: Contribution to journalArticle

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)467-483
    Number of pages17
    JournalBulletin of the Malaysian Mathematical Sciences Society
    Volume42
    Issue number2
    DOIs
    Publication statusPublished - 15 Mar 2019

    Keywords

    • Accretive mapping
    • Common fixed point
    • Explicit method
    • Nonexpansive semigroup
    • Variational inequality

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