On some variants of Schu’s lemma

Abstract In this note, we demonstrate that an incorrect statement has been propagated in multiple papers, stemming from the substitution of “lim” with “limsup” for a sequence in Lemma 1.3 of the paper [J. Schu: Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43(1), 153–159 (1991). This occurred over a span of more than 20 years, with the earliest paper we identified using this incorrect statement dating back to 2002.