In this article, we study the extended split equality problem and extended split equality fixed point problem, which are extensions of the convex feasibility problem. For solving the extended split equality problem, we present two self-adaptive stepsize algorithms with internal perturbation projection and obtain the weak and the strong convergence of the algorithms, respectively. Furthermore, based on the operators being quasinonexpansive, we offer an iterative algorithm to solve the extended split equality fixed point problem. We introduce a way of selecting the stepsize which does not need any prior information about operator norms in the three algorithms. We apply our iterative algorithms to some convex and nonlinear problems. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithms.

中文翻译：

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扩展拆分等式问题和扩展拆分等式不动点问题的内部摄动投影算法

在本文中，我们研究了扩展拆分等式问题和扩展拆分等式不动点问题，它们是凸可行性问题的扩展。为了解决扩展的分裂等式问题，我们提出了两种具有内部扰动投影的自适应步长算法，分别获得了算法的弱收敛性和强收敛性。此外，基于算子是拟扩张的，我们提供了一种迭代算法来解决扩展的等式不动点问题。我们介绍了一种选择逐步大小的方法，该方法不需要三种算法中有关算子范数的任何先验信息。我们将迭代算法应用于一些凸和非线性问题。最后，一些数值结果表明了所提算法的可行性和有效性。