Split Generalized Equilibrium Problem Research Articles

An iterative approximation scheme for solving a split generalized equilibrium, variational inequalities and fixed point problems

ABSTRACTIn this paper, we consider a common solution of three problems in Hilbert spaces including the split generalized equilibrium problem, the variational inequality problem and fixed point problem. For finding the solution, we present a new iterative method and prove the strongly convergence theorem under mild conditions. Moreover, some numerical examples are given in the last section.

A new Hybrid Projection Algorithm for Solving the Split Generalized Equilibrium Problems and the System of Variational Inequality Problems

In this paper, we introduced modified Mann iterative algorithms by the new hybrid projection method for finding a common element of the set of fixed points of a countable family of nonexpansive mappings, the set of the split generalized equilibrium problem and the set of solutions of the general system of the variational inequality problem for two-inverse strongly monotone mappings in real Hilbert spaces. The strong convergence theorem of the iterative algorithm in Hilbert spaces under certain mild conditions are provided.

Iterative approximation of a common solution of a split generalized equilibrium problem and a fixed point problem for nonexpansive semigroup

Purpose: In this paper, we introduce and study an iterative method to approximate a common solution of a split generalized equilibrium problem and a fixed point problem for a nonexpansive semigroup in real Hilbert spaces. Methods: We prove a strong convergence theorem of the iterative algorithm in Hilbert spaces under certain mild conditions. Results: We obtain a strong convergence result for approximating a common solution of a split generalized equilibrium problem and a fixed point problem for a nonexpansive semigroup in real Hilbert spaces, which is a unique solution of a variational inequality problem. Further, we obtain some consequences of our main result. Conclusions: The results presented in this paper are the supplement, extension, and generalization of results in the study of Plubtieng and Punpaeng and that of Cianciaruso et al. The approach of the proof given in this paper is also different.