ABSTRACT

In this article we introduce an inertial iterative scheme with self-adaptive step size for finding a common solution of split common null point problem for a finite family of maximal monotone operators and fixed point problem for a finite family of multivalued demicontractive mappings between a Banach space and Hilbert space. Strong convergence result is obtained for the proposed algorithm. The self-adaptive step size ensures no requirement for a prior knowledge or estimate of the norm of the operator. The inertial term introduced in the algorithm is efficient, it helps to avoid imposing some strong conditions usually used for inertial-type algorithms by many authors. We give some applications of our results to game theory, split equilibrium and minimum-norm problems. Numerical experiment is also presented to demonstrate the efficiency of our proposed method as well as comparing with other existing method in the literature. Our results improve and generalize many well known results in this direction in the literature.

摘要

在本文中，我们介绍了一种具有自适应步长的惯性迭代方案，用于寻找有限的最大单调算子族的分裂公共零点问题的公共解决方案和巴纳赫空间之间的有限多值去收缩映射的不动点问题的公共解决方案和希尔伯特空间。所提算法获得了较强的收敛效果。自适应步长确保不需要先验知识或估计算子的规范。算法中引入的惯性项是有效的，它有助于避免强加一些通常被许多作者用于惯性类型算法的强条件。我们将我们的结果应用于博弈论、分裂均衡和最小范数问题。还提出了数值实验来证明我们提出的方法的效率以及与文献中其他现有方法的比较。我们的结果改进并概括了文献中这个方向的许多众所周知的结果。