Convergence of ergodic means of orbits of semigroups of nonexpansive mappings in sets with the \(\varGamma\)-Opial property (Q2373845)

The authors generalize a \textit{T.\,Suzuki}'s result [Nonlinear Anal., Theory Methods Appl.\ 58, No.\,3--4 (A), 441--458 (2004; Zbl 1068.47078)] on the set of common fixed points of one-parameter semigroups of nonexpansive mappings in Banach spaces with the Opial property. As an application, they construct an ergodic nonexpansive retraction onto the common fixed point set of a nonexpansive semigroup.