Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 174318, 20 pages.

General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities

Nopparat Wairojjana and Poom Kumam

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 174318, 20 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357179969

Digital Object Identifier
doi:10.1155/2012/174318

Mathematical Reviews number (MathSciNet)
MR2948145

Zentralblatt MATH identifier
1251.49012

Citation

Wairojjana, Nopparat; Kumam, Poom. General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities. J. Appl. Math. 2012, Special Issue (2012), Article ID 174318, 20 pages. doi:10.1155/2012/174318. https://projecteuclid.org/euclid.jam/1357179969


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