General iterative algorithms for hierarchical fixed points approach to variational inequalities

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.