Nonlinear Analysis and Convex Analysis by fixed point theory and its Application to Equilibrium problems and Nonlinear Optimization

在这项研究中，我们利用不动点理论，在非线性分析和凸分析中得到了许多新的和重要的非线性问题的定理。例如，我们研究了公共吸引点，证明了不具凸性的非扩张半群的非线性遍历定理。证明了非扩张半群的公共吸引点的强收敛。进一步，利用Halpern型和Browder型迭代法证明了Banach空间中一致渐近正则非扩张半群的强收敛定理。

In this study, we obtain many new and important theorems for nonlinear problems in nonlinear analysis and convex analysis by using fixed point theory. For example, we studied common attractive points and proved nonlinear ergodic theorems for nonexpansive semigroups without convexity. And, we proved strong convergence to common attractive points of nonexpansive semigroups. Further, we proved strong convergence theorems for uniformly asymptotically regular nonexpansive semigroup in Banach spaces by Halpern type and Browder type iterations.