This paper deals with a split equality equilibrium problem for pseudomonotone bifunctions and a split equality hierarchical fixed point problem for nonexpansive and quasinonexpansive mappings. We suggest and analyze an iterative scheme where the stepsizes do not depend on the operator norms, the so-called simultaneous projected subgradient-proximal iterative scheme for approximating a common solution of the split equality equilibrium problem and the split equality hierarchical fixed point problem. Further, we prove a weak convergence theorem for the sequences generated by this scheme. Furthermore, we discuss some consequences of the weak convergence theorem. We present a numerical example to justify the main result.

本文讨论了伪单调双功能的等式分裂等式问题和非扩张和拟锥扩展映射的等式分层不动点问题。我们建议并分析一种迭代方案，其中步长不依赖于算子范数，即所谓的同时投影次梯度-近邻迭代方案，用于近似分裂等式平衡问题和分裂等式分层不动点问题的通用解。此外，我们证明了该方案生成的序列的弱收敛定理。此外，我们讨论了弱收敛定理的一些后果。我们提供一个数值示例来证明主要结果。