Mosco convergence of the sets of fixed points for one-parameter nonexpansive semigroups (Q927956)

The author proves the Mosco convergence of the sets of fixed points for one-parameter nonexpansive semigroups \(T(t)\) on a closed convex set of a Banach space with the Opial property. Namely, under the assumption that \(t_n>\tau\geq 0\), \(t_n\to\tau\) as \(n\to\infty\), it is established that the sets of fixed points of \(T(t_n)\) converge in the sense of Mosco to the set of common fixed points of the semigroup \(T(t)\).