Banach空间上非线性映照的遍历收敛定理

Ergodic Convergence Theorem for Nonlinear Mappings in Banach Spaces

X是Banach空间,(X,τ)是局部凸线性拓扑空间,C是X上的τ-序列紧凸集,T是C上的渐近非扩张映照并且具有性质(Γ)．在一致τ-opial条件下给出了渐近非扩张映照的遍历收敛定理并进行了证明．该结论首次在Banach空间中给出了遍历收敛定理,因而定理推广了近期相关的一系列研究成果．

Let X be a Banach space, （X,τ） a local convex linear topological space, C a τ-sequence compact convex subset of X, and T an asymptotically nonexpansive mapping with the property （P） from C to itself, we give the ergodic convergence theorem for asymptotically nonexpansive mapping under uniformly τ-opial condition. Result presented in this paper is the first ergodic convergence theorem in Banach space; therefore it further expands recent related results in other researches.