On error bounds for fixed point problems and its applications

这项研究旨在开发解决不动点问题的有效算法。特别地，我们研究了保证由迭代方法生成的序列在有限步内获得精确解的概念。首先，基于求解凸规划问题的理论技巧，我们给出了集值映射的一个新条件。进一步，利用这些结果，我们得到了凸极小化问题和变分不等式等非线性问题的有限收敛结果。

This research aims to develop efficient algorithms for solving fixed point problems. Especially, we investigated notions that guarantee sequences generated by iterative methods can obtain an exact solution in finite number of steps. First, we provided a new condition for set-valued mappings based on theoretical techniques for solving the convex programming problem. Further, by using these results, we derived finite convergence results concerning nonlinear problems such as the convex minimization problem and the variational inequality.