Study of equilibrium problems and its application to optimization problems

在这项研究中，我们讨论了Banach空间和Hilbert空间中的平衡问题、不动点问题、零点问题和变分不等式问题。然后利用不动点理论和非线性算子理论的方法得到了这类问题的一些存在定理和收敛定理。此外，我们还研究了不动点逼近方法与非线性映射的强非扩张性或强非扩张性之间的关系。

In this research, we dealt with equilibrium problems, fixed point problems, zero point problems, and variational inequality problems in Banach spaces and Hilbert spaces. Then we obtained some existence theorems and convergence theorems for such problems by using the method of fixed point theory and nonlinear operator theory. Moreover, we also investigated relationships between approximation methods of fixed points, and strong or firm nonexpansiveness of nonlinear mappings.