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<p>We give a sufficient condition of Cauchy sequence with contraction constant <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3289_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>λ</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$\lambda \in (0, 1)$</EquationSource> </InlineEquation> in fuzzy <i>b</i>-metric spaces, which is a positive answer to the open question proposed by Rakić et al. (J. Inequal. Appl. 2020:99, <CitationRef CitationID="CR16">2020</CitationRef>). Thus we simplify the proofs of many fixed point theorems in fuzzy <i>b</i>-metric spaces. Applying this result, we obtain two single-valued fixed point results and a set-valued fixed point result for Banach type in fuzzy <i>b</i>-metric spaces, which improve and extend the relevant results in the literature.</p>

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Answer to a question on Cauchy sequence in fuzzy b-metric spaces and its applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月25日

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  • Shumin Lu,
  • Ning Lu,
  • Jianying Zhang,
  • Fei He

摘要

We give a sufficient condition of Cauchy sequence with contraction constant λ ∈ ( 0 , 1 ) $\lambda \in (0, 1)$ in fuzzy b-metric spaces, which is a positive answer to the open question proposed by Rakić et al. (J. Inequal. Appl. 2020:99, 2020). Thus we simplify the proofs of many fixed point theorems in fuzzy b-metric spaces. Applying this result, we obtain two single-valued fixed point results and a set-valued fixed point result for Banach type in fuzzy b-metric spaces, which improve and extend the relevant results in the literature.