General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities
Nopparat Wairojjana, Poom Kumam · Journal of Applied Mathematics · 2012
This paper deals with new methods for approximating a solution to the fixed point problem; find , 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 , , 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 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.