General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities - Nopparat Wairojjana; Poom Kumam (Journal of Applied Mathematics)
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 γ̅>0, 0<γ<γ̅/ρ, T is a nonexpansive mapping on C, and PF(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.