【摘要】 讨论了一类集值映射的半闭性及不动点的弱收敛性 ,得到以下结论 :若X为满足局部一致Opial条件的Banach空间 ,T为X中非空弱紧凸子集上的连续集值渐近非扩张映射 ,则I -T在点 0是半闭的 .本文还分别讨论了满足局部一致Opial条件和满足一致Opial条件的Banach空间中这类映射的不动点的弱收敛 ,从而把单值渐近非扩张映射情形推广到集值渐近非扩张映射情形 .更多还原

【Abstract】 This paper discusses the demiclosedness principle and weak convergence of the multi_valued asymptotically non_expansive mappings. It reaches the conclusion that if T is the continuous multi_valued asymptotically non_expansive mapping on the nonempty weakly compact convex subset of a Banach space satisfying the locally uniform Opial condition, then I-T is demiclosed at zero. The weak convergence of the fixed point of multi_valued asymptotically non_expansive mappings on the nonempty weakly compact convex subset of a Banach space satisfying locally uniform Opial condition or uniform Opial condition is also discussed. Some results of asymptotically non_expansive mappings are generalized.更多还原