General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities

[摘要] This paper deals with new methods for approximating a solution to the fixed point problem; findx̃∈F(T), whereHis a Hilbert space,Cis a closed convex subset ofH,fis aρ-contraction fromCintoH,0<ρ<1,Ais a strongly positive linear-bounded operator with coefficientγ̅>0,0<γ<γ̅/ρ,Tis a nonexpansive mapping onC,andPF(T)denotes the metric projection on the set of fixed point ofT. 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〉≥0forx∈F(T), whereτ∈[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.

[学科分类] 应用数学