Let G be a semitopological semigroup. Let C be a nonempty subset of a Hilbert space and J ={T t:t∈G} be a representation of G as asymptotically nonexpansive type mappings of C into itself such ...Let G be a semitopological semigroup. Let C be a nonempty subset of a Hilbert space and J ={T t:t∈G} be a representation of G as asymptotically nonexpansive type mappings of C into itself such that the common fixed point set F(J) of J in C is nonempty. It is proved that ∩s∈G co {T ts x:t∈G}∩F(J) is nonempty for each x ∈ C if and only if there exists a nonexpansive retraction P of C onto F(J) such that PT s=T sP=P for all s∈G and P(x) is in the closed convex hull of {T sx:s∈G}, x∈C . This result shows that many key conditions in [1-4, 9, 12-15 ] are not necessary.展开更多
文摘Let G be a semitopological semigroup. Let C be a nonempty subset of a Hilbert space and J ={T t:t∈G} be a representation of G as asymptotically nonexpansive type mappings of C into itself such that the common fixed point set F(J) of J in C is nonempty. It is proved that ∩s∈G co {T ts x:t∈G}∩F(J) is nonempty for each x ∈ C if and only if there exists a nonexpansive retraction P of C onto F(J) such that PT s=T sP=P for all s∈G and P(x) is in the closed convex hull of {T sx:s∈G}, x∈C . This result shows that many key conditions in [1-4, 9, 12-15 ] are not necessary.
