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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 (1991), 153--159]. This occurred over a span of more than 20 years, with the earliest paper we identified using this incorrect statement dating back to 2002., Comment: The paper has now 19 pages and contains 211 references. Having in view that Prof. R.I. Bot made some important remarks on the previous version of the paper, I (C. Zalinescu) invited him to become co-author of this work and I am very satisfied that he accepted