Search

In this paper, we propose an iterative algorithm to find the common element of set of solutions of a split equilibrium problem and set of fixed points of an asymptotically nonexpansive mapping in Hilbert spaces. The new method is used to prove the strong convergence for the result of this paper. The result extends the corresponding one in the literature. [ABSTRACT FROM AUTHOR]

In this paper, an iterative algorithm is investigated for a common solution problem. Strong convergence of the algorithm is obtained in the framework of real Hilbert spaces. Applications are also provided to support the main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative scheme for finding a common element of the set of common solutions of a finite family of equilibrium problems with relaxed monotone mappings, of the set of common solutions of a finite family of variational inequalities and of the set of common fixed points of an infinite family of nonexpansive mappings in a Hilbert space. Strong convergence for the proposed iterative scheme is proved. As an application, we solve a multi-objective optimization problem using the result of this paper. Our results improve and extend the corresponding ones announced by others. [ABSTRACT FROM AUTHOR]

Let H be a Hilbert space and let and be the countable families of nonexpansive mappings of H into itself such that . Assume that F is a nonlinear operator which is κ-Lipschitzian and η-strong monotone on C. In this article, we devise a new iterative scheme {x n } from an arbitrary initial point x 0∈H for the countable family of nonexpansive mappings and and prove that {x n } strongly converges to the unique solution x* of the variational inequality Applications to constrained generalized pseudoinverse are included. [ABSTRACT FROM AUTHOR]

Abstract: Recently, Ceng, Guu and Yao introduced an iterative scheme by viscosity-like approximation method to approximate the fixed point of nonexpansive mappings and solve some variational inequalities in Hilbert space (see Ceng et al. (2009) ). Takahashi and Takahashi proposed an iteration scheme to solve an equilibrium problem and approximate the fixed point of nonexpansive mapping by viscosity approximation method in Hilbert space (see Takahashi and Takahashi (2007) ). In this paper, we introduce an iterative scheme by viscosity approximation method for finding a common element of the set of a countable family of nonexpansive mappings and the set of an equilibrium problem in a Hilbert space. We prove the strong convergence of the proposed iteration to the unique solution of a variational inequality. [Copyright &y& Elsevier]