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Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T : C → C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover , we prove that if T is uniformly L-Lipschitzian and completely continuous, then the iterative scheme… (More)

In this paper, to find a common element of the fixed point set of common fixed points of a countable family of nonexpansive mappings and the solution set of the variational inequality for α-inverse-strongly monotone, we introduce an iterative approximation method in a real Hilbert space. Then the strong convergence theorem is proved under some appropriate… (More)

Recommended by Pavel Drabek We construct implicit random iteration process with errors for a common random fixed point of a finite family of asymptotically quasi-nonexpansive random operators in uniformly convex Banach spaces. The results presented in this paper extend and improve the corresponding results of Beg and Abbas in 2006 and many others.

- Rabian Wangkeeree, Panu Yimmuang
- 2013

In this paper, we introduce and study a new class of generalized nonlinear vector mixed quasi-variational-like inequalities governed by a multi-valued map in Hausdorff topological vector spaces which includes generalized vector mixed general quasi-variational-like inequalities, generalized nonlinear mixed variational-like inequalities, and so on. By using… (More)

- Rabian Wangkeeree, Pakkapon Preechasilp
- 2012

In this paper, we introduce the modified general iterative approximation methods for finding a common fixed point of nonexpansive semigroups which is a unique solution of some variational inequalities. The strong convergence theorems are established in the framework of a reflexive Banach space which admits a weakly continuous duality mapping. The main… (More)

Viscosity approximation methods for nonexpansive nonself-mappings are studied. Let C be a nonempty closed convex subset of Hilbert space H, P a metric projection of H onto C and let T be a nonexpansive nonself-mapping from C into H. For a contraction f on C and {t n } ⊆ (0,1), let x n be the unique fixed point of the contraction x → t n f (x) + (1 − t… (More)

Keywords: Mixed quasi-variational-like inequality problem Auxiliary principle technique Cocoercive mapping Strongly monotone mapping a b s t r a c t In this paper, some existence theorems for the mixed quasi-variational-like inequalities problem in a reflexive Banach space are established. The auxiliary principle technique is used to suggest a novel and… (More)

- Rattanaporn Wangkeeree, Rabian Wangkeeree, Anthony To, Ming Lau
- 2009

We introduce an iterative scheme for finding a common element of the set of fixed points of a k-strictly pseudocontractive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping, and the set of solutions of the mixed equilibrium problem in a real Hilbert space. Under suitable conditions, some strong convergence… (More)