Mean ergodic theorems for semigroups of linear operators in \(p\)-Banach spaces (Q2792519)

In the late 1930's, \textit{K. Yosida} [Proc. Imp. Acad. Japan 14, 292--294 (1938; Zbl 0019.41403)] proved a mean ergodic theorem for linear operators. \textit{J.-B. Baillon} [C. R. Acad. Sci., Paris, Sér. A 280, 1511--1514 (1975; Zbl 0307.47006)] proved the first nonlinear ergodic theorem which recently has been studied by Rodé and Takahashi. Both tried to extend Baillon's result by generalizing Cesàro means. In this work, the authors use the ideas and methods of Yosida [loc. cit.], \textit{F. P. Greenleaf} [Invariant means on topological groups and their applications. London: Van Nostrand Reinhold Company (1969; Zbl 0174.19001)], \textit{G. Rodé} [J. Math. Anal. Appl. 85, 172--178 (1982; Zbl 0485.47041)] and \textit{N. Hirano} and \textit{W. Takahashi} [Pac. J. Math. 112, 333--346 (1984; Zbl 0544.47055); \textit{W. Takahashi}, Kōdai Math. Semin. Rep. 23, 131--143 (1971; Zbl 0219.47035)] to extend Yosida's theorem to semigroups of linear operators in \(p\)-Banach spaces; they use also the ideas of \textit{K. Kido} and \textit{W. Takahashi} [J. Math. Anal. Appl. 103, 387--394 (1984; Zbl 0608.47045)] as a base for their results.