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Fundamental Questions and New Counterexamples for b -Metric Spaces and Fatou Property

Author

Listed:
  • Ning Lu

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

  • Fei He

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

  • Wei-Shih Du

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan)

Abstract

In this paper, we give new examples to show that the continuity actually strictly stronger than the Fatou property in b -metric spaces. We establish a new fixed point theorem for new essential and fundamental sufficient conditions such that a Ćirić type contraction with contraction constant λ ∈ [ 1 s , 1 ) in a complete b -metric space with s > 1 have a unique fixed point. Many new examples illustrating our results are also given. Our new results extend and improve many recent results and they are completely original and quite different from the well known results on the topic in the literature.

Suggested Citation

  • Ning Lu & Fei He & Wei-Shih Du, 2019. "Fundamental Questions and New Counterexamples for b -Metric Spaces and Fatou Property," Mathematics, MDPI, vol. 7(11), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1107-:d:287113
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    References listed on IDEAS

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    1. Fei He, 2014. "Common Fixed Points for Nonlinear Quasi-Contractions of Ćirić Type," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, July.
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