Hierarchical equilibrium and generalized variational inequality problems

Conference proceedings article

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Publication Details

Author list: Wairojjana N., Kumam P.

Publisher: Springer Science Business Media

Publication year: 2014

Volume number: 275 LNEE

Start page: 341

End page: 357

Number of pages: 17

ISBN: 9789400776838

ISSN: 1876-1100

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84958541439&doi=10.1007%2f978-94-007-7684-5_24&partnerID=40&md5=14e8bd5e7100312d8e924a1d9bf0a1cd

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we study the convex feasibility problem (CFP) in the case that each is a solution set of the generalized variational inequality and the equilibrium problem and introduce a new approach method to find a common element in the intersection of the set of the solutions of a finite family of equilibrium problems and the intersection of the set of the solutions of a finite family of generalized variational inequality problems in a real Hilbert space which is a unique solution of the hierarchical equilibrium and generalized variational inequality problems(HEGVIP). Under appropriate conditions, some strong convergence theorems are established. Our results generalize and improve the corresponding results of Wairojjana and Kumam (2013) [27] and some authors. ฉ 2014 Springer Science+Business Media Dordrecht.

Keywords

Convex feasibility problem, Generalized variational inequality problem, Hierarchical fixed point problem, Hierarchical generalized variational inequality problem, Hilbert space