论文信息 - The split equilibrium problem and its convergence algorithms

The split equilibrium problem and its convergence algorithms

The purpose of this paper is to introduce a split equilibrium problem (SEP) and find a solution of the equilibrium problem such that its image under a given bounded linear operator is a solution of another equilibrium problem. By using the iterative method, we construct some iterative algorithms to solve such problem in real Hilbert spaces and obtain some strong and weak convergence theorems. Finally, we point out that there exist many SEPs which need the use of new methods to solve them. Some examples are given to illustrate our results.MSC:47J25, 47H09, 65K10.

Zhenhua He | Zhenhua He

[1] H. Kunzi,et al. Lectu re Notes in Economics and Mathematical Systems , 1975 .

[2] Chi Kin Chan,et al. A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization , 2009 .

[3] A. Moudafi,et al. Proximal and Dynamical Approaches to Equilibrium Problems , 1999 .

[4] Giuseppe Marino,et al. An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings , 2009 .

[5] Yair Censor,et al. Algorithms for the Split Variational Inequality Problem , 2010, Numerical Algorithms.

[6] Shahram Saeidi,et al. Iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings , 2009 .

[7] P. L. Combettes,et al. Equilibrium programming in Hilbert spaces , 2005 .

[8] Zhenhua He,et al. Strong convergence theorems for equilibrium problems and fixed point problems: A new iterative method, some comments and applications , 2011 .