General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities

Nopparat Wairojjana and Poom Kumam

Journal of Applied Mathematics, 2012, vol. 2012, 1-20

Abstract:

This paper deals with new methods for approximating a solution to the fixed point problem; find x ̃ ∈ 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 γ ̅ > 0 , 0 < γ < γ ̅ / 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 - γ f ) x ̃ + τ ( I - S ) x ̃ , x - x ̃ 〉 ≥ 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.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/JAM/2012/174318.pdf (application/pdf)
http://downloads.hindawi.com/journals/JAM/2012/174318.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:174318

DOI: 10.1155/2012/174318

Access Statistics for this article

More articles in Journal of Applied Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().