The paper considers a split inverse problem involving component equilibrium problems in Hilbert spaces. This problem therefore is called the split equilibrium problem (SEP). It is known that almost solution methods for solving problem (SEP) are designed from two fundamental methods as the proximal point method and the extended extragradient method (or the two-step proximal-like method). Unlike previous results, in this paper we introduce a new algorithm, which is only based on the projection method, for finding solution approximations of problem (SEP), and then establish that the resulting algorithm is weakly convergent under mild conditions. Several of numerical results are reported to illustrate the convergence of the proposed algorithm and also to compare with others.

中文翻译：

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解决分裂均衡问题的投影方法

本文考虑了希尔伯特空间中涉及分量平衡问题的分裂逆问题。因此，此问题称为分裂均衡问题（SEP）。众所周知，解决问题的几乎解决方法（SEP）是从两种基本方法设计而成的，即近点方法和扩展的梯度方法（或两步式类似近端的方法）。与以前的结果不同，本文介绍了一种仅基于投影方法的新算法，用于查找问题的解近似值（SEP），然后确定所得算法在温和条件下是弱收敛的。报告了一些数值结果，以说明该算法的收敛性，并与其他算法进行比较。