General iterative method for convex feasibility problem via the hierarchical generalized variational inequality problems

Conference proceedings article

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Publication Details

Author list: Wairojjana N., Kumam P.

Publication year: 2013

Volume number: 2203

Start page: 1129

End page: 1134

Number of pages: 6

ISBN: 9789881925268

ISSN: 2078-0958

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84880051408&partnerID=40&md5=d56b80a16d2ac4d1cfcf0cb0757047ac

Languages: English-Great Britain (EN-GB)

Abstract

Let C be a nonempty closed and convex subset of a real Hilbert space H. Let Am;Bm : C → H be relaxed cocoercive mappings for each 1 ≤ m le; r, where r ≥ 1 is integer. Let f : C → C be a contraction with coefficient k ∈ (0; 1). Let G : C → C be ξ-strongly monotone and L-Lipschitz continuous mappings. Under the assumption ∩r m=1GV I(C;Bm;Am) ≠ φ where GV I(C;B m;Am) is the solution set of a generalized variational inequality. Consequently, we prove a strong convergence theorem for finding a point x̃ ∈ ∩r m=1GV I(C;Bm;A m) which is a unique solution of the hierarchical generalized variational inequality ((γf - μG)x̃, x-x̃) ≤ 0, ∀x ∈ ∩r m=1GV I(C;Bm;Am).

Keywords

Convex feasibility problem, Generalized variational inequality problem, Hierarchical generalized variational inequality problem, Relaxed cocoercive mapping