CAJ | 학술논문

设G为半群,C为具Fréchet可微范数的一致凸Banach空间X的非空有界闭凸子集.(s)={Tn:t∈G}为C上到自身的渐近非扩张型半群,且F((s))非空.在本文中,我们证明了:对(s)的任一殆轨道u(.),∩ c-o{u(ts),t∈G)∩F(S)至多为单点集.进一步,对x∈C,s∈G∩s∈G c-o{Tsx,t∈G}∩F((s))非空当且仅当存在C到F((s))上非扩张压缩P,使得对任意t∈G,PTt =TtP=P,Px∈c-o{ Ttx,t∈G}.这一结果不仅推广了许多已知结果,而且说明它们中的一些关键条件是不必要的.
설G위반군,C위구Fréchet가미범수적일치철Banach공간X적비공유계폐철자집.(s)={Tn:t∈G}위C상도자신적점근비확장형반군,차F((s))비공.재본문중,아문증명료:대(s)적임일태궤도u(.),∩ c-o{u(ts),t∈G)∩F(S)지다위단점집.진일보,대x∈C,s∈G∩s∈G c-o{Tsx,t∈G}∩F((s))비공당차부당존재C도F((s))상비확장압축P,사득대임의t∈G,PTt =TtP=P,Px∈c-o{ Ttx,t∈G}.저일결과불부추엄료허다이지결과,이차설명타문중적일사관건조건시불필요적.
Let G be a semigroup.Let C be a nonempty bounded closed convex subset of a uniformly convex Banach space X with a Fréchet differentiable norm and (s) ={Tt:t ∈ G} be a semigroup of asymptotically nonexpansive type mappings on C with F(s) ≠ θ.We prove in this paper that for every almost orbit u(.) of (s),∩s∈G c-o{ u( ts ),t ∈ G} ∩ F ((s) ) consists of at most one point.Further,∩s∈G c-o{ Ttsx,t ∈G} ∩ F(（s）) is nonempty for each x ∈ C if and only if there exists a nonexpansive retraction P of C onto F((s)) such that PTt =TtP =P for all t ∈ G and Px ∈c-o{Ttx,t ∈ G}.This result not only gengneralizes some well-known theorems,but also shows that some key conditions in them are not necessary.