一般Banach空间中渐近非扩张型半群的不动点定理

Fixed Point Theorems for Asymptotically Nonexpansive Type Semigroups in General Banach Spaces

该文首先在一般Banach空间中对渐近非扩张型半群证明了两个不动点存在定理,并由此给出了渐近非扩张型半群Mann型迭代序列的强收敛定理.该文的主要结果将Suzuki和Takahashi的相应结果推广到non-Lipschitzian半群情形.

This paper is first devoted to proving two existence theorems of fixed points for asymptotically nonexpansive type semigroups in general Banach spaces. Based on these results, a strong convergence theorem of Mann＇s type sequences for the asymptotically nonexpansive type semigroups is given. The main results extend the results of Suzuki and Takahashi to the case of the non-Lipschitzian semigroups.