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<p>In this paper, we establish Kannan-type, Reich-type, and Ćirić-type fixed point theorems in complete regular semimetric spaces with strong triangle functions, thereby providing an affirmative answer to an open question posed by Nguyen and Vo [<CitationRef CitationID="CR17">17</CitationRef>]. Furthermore, two counterexamples are constructed: one illustrates that the Ćirić-type fixed point theorem is not valid in the more general setting of regular semimetric spaces with triangle functions, and the other shows that Suzuki’s lemma does not hold in this setting.</p>

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Answers to a question on fixed point existence in regular semimetric spaces with strong triangle functions

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Shumin Lu,
  • Ning Lu,
  • Fei He

摘要

In this paper, we establish Kannan-type, Reich-type, and Ćirić-type fixed point theorems in complete regular semimetric spaces with strong triangle functions, thereby providing an affirmative answer to an open question posed by Nguyen and Vo [17]. Furthermore, two counterexamples are constructed: one illustrates that the Ćirić-type fixed point theorem is not valid in the more general setting of regular semimetric spaces with triangle functions, and the other shows that Suzuki’s lemma does not hold in this setting.