General iterative algorithms for hierarchical fixed points approach to variational inequalities

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Wairojjana N., Kumam P.

Publisher: Hindawi

Publication year: 2012

Journal: Journal of Applied Mathematics (1110-757X)

Volume number: 2012

ISSN: 1110-757X

eISSN: 1687-0042

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84864930545&doi=10.1155%2f2012%2f174318&partnerID=40&md5=1b08df8bac75c8ee37a1f48130e87a26

Languages: English-Great Britain (EN-GB)

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Abstract

This paper deals with new methods for approximating a solution to the fixed point problem; find x̃ ∈ F(T), where H is a Hilbert space, C is a closed convex subset of H, f is a ρ-contraction from C into H, 0 < ρ < 1, A is a strongly positive linear-bounded operator with coefficient γ̄ > 0, 0 < γ < γ̄/ρ, T is a nonexpansive mapping on C, and P F(T) denotes the metric projection on the set of fixed point of T. Under a suitable different parameter, we obtain strong convergence theorems by using the projection method which solves the variational inequality 〈(A - γf)x̃+τ(I-S)x̃,x- x̃〉 ≥ 0 for x ∈ F(T), where τ ∈ [0, ∞). Our results generalize and improve the corresponding results of Yao et al. (2010) and some authors. Furthermore, we give an example which supports our main theorem in the last part. Copyright © 2012 Nopparat Wairojjana and Poom Kumam.

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