Banach空间中渐近非扩张型半群的遍历定理

Ergodic Theorem for the Semi-group of Asymptotically Nonexpansive Type Mappings in Banach Spaces

对带Opial条件的Banach空间中非扩张半群的不动点理论进行推广,得到了带Opial条件的Banach空间中渐近非扩张型半群的遍历收敛定理.

This paper proves ergodic theorem for the semi-group of asymptotically nonexpansive type mappings in Banach spaces with the Opial property.Suppose E is a Banach space with the Opial property,C is a weak compact and convex subset of E and T={T（t）：t≥0} is an asymptotically nonexpansive type semi-group of C.If M（τβ,z）→^wz for z∈C,then T（t）z→w^z.