Banach空间中渐近正则半群的不动点定理

FIXED POINT THEOREMS FOR ASYMPTOTICALLY REGULARY SEMIGROUPS IN BANACH SPACES

设X是p一致凸Banach空间,具有弱一致正规结构与非严格的Opial性质.又设C是X的非空凸弱紧子集.在适当的条件下,证明了C上每个渐近正则半群T={T(t):t∈S}都有不动点进一步,在类似的条件下,也讨论了一致凸Banach空间中渐近正则半群的不动点的存在性.

Let X be a p-uniformly convex Banach space with both the weak uniformly normal structure and the non-strict Opial property, and C a nonempty convex weakly compact subset of X. The existence of fixed points for each asymptotically regular semigroup T = {T(t) : t∈5} on C is proved under some suitable conditions. Further, under the similar conditions, the author discusses the existence of fixed points for asymptotically regular semigroup in a uniformly convex Banach space.