In this paper, we propose two strongly convergent algorithms which combines diagonal subgradient method, projection method and proximal method to solve split equilibrium problems and split common fixed point problems of nonexpansive mappings in a real Hilbert space: fixed point set constrained split equilibrium problems (FPSCSEPs) in real Hilbert spaces. The computations of first algorthim requires prior knowledge of operator norm. To estimate the norm of an operator is not always easy, and if it is not easy to estimate the norm of an operator, we purpose another iterative algorithm with a way of selecting the step-sizes such that the implementation of the algorithm does not need any prior information as regards the operator norm. The strong convergence properties of the algorithms are established under mild assumptions on equilibrium bifunctions. We also report some applications and numerical results to compare and illustrate the convergence of the proposed algorithms.

中文翻译：

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求解Hilbert空间中非扩张映射的分裂均衡问题和分裂公共不动点问题的混合投影次梯度近邻算法

在本文中，我们提出了两种强收敛算法，它们结合对角线次梯度法，投影法和近端法来解决实际希尔伯特空间中的非平衡映射的分裂均衡问题和分裂公共不动点问题：不动点集约束分裂均衡问题（FPSCSEPs ）在真实的希尔伯特空间中。第一算法的计算需要算子范数的先验知识。估计一个算子的范数并不总是那么容易，并且如果不容易估计一个算子的范数，我们将目标定为另一种迭代算法，其选择步长的方式使得该算法的实现不需要有关运营商规范的任何先前信息。该算法的强收敛性是在对平衡双功能的温和假设下建立的。