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<p>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.</p>

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On some variants of Schu’s lemma

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  • 发表日期：

    2025年10月10日

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  • R. I. Boţ,
  • C. Zălinescu

摘要

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.