The hybrid steepest descent method for solving variational inequality over triple hierarchical problems

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

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Publication Details

Author list: Wairojjana N., Jitpeera T., Kumam P.

Publisher: SpringerOpen

Publication year: 2012

Journal: Journal of Inequalities and Applications (1025-5834)

Volume number: 2012

ISSN: 1025-5834

eISSN: 1029-242X

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84902584469&doi=10.1186%2f1029-242X-2012-280&partnerID=40&md5=214d7e98b2601a12b4ac97d5fb4a8e74

Languages: English-Great Britain (EN-GB)

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Abstract

An explicit algorithm is introduced to solve the monotone variational inequality over a triple hierarchical problem. The strong convergence for the proposed algorithm to the solution is guaranteed under some assumptions. Our results extend those of Iiduka (Nonlinear Anal. 71:e1292-e1297, 2009), Marino and Xu (J. Optim. Theory Appl. 149(1):61-78, 2011), Yao et al. (Fixed Point Theory Appl. 2011:794203, 2011) and other authors. ฉ 2012 Wairojjana et al.; licensee Springer.

Keywords

Hierarchical fixed point, Lipchitz continuous, Strongly monotone mapping, Strongly positive linear bounded operator