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Generalized Metric Spaces Do Not Have the Compatible Topology

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  • Tomonari Suzuki

Abstract

We study generalized metric spaces, which were introduced by Branciari (2000). In particular, generalized metric spaces do not necessarily have the compatible topology. Also we prove a generalization of the Banach contraction principle in complete generalized metric spaces.

Suggested Citation

  • Tomonari Suzuki, 2014. "Generalized Metric Spaces Do Not Have the Compatible Topology," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, August.
    • Handle: RePEc:hin:jnlaaa:458098
    DOI: 10.1155/2014/458098
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    Cited by:

    1. Hassen Aydi & Chi-Ming Chen & Erdal Karapınar, 2019. "Interpolative Ćirić-Reich-Rus Type Contractions via the Branciari Distance," Mathematics, MDPI, vol. 7(1), pages 1-7, January.
    2. Kamaleldin Abodayeh & Erdal Karapınar & Ariana Pitea & Wasfi Shatanawi, 2019. "Hybrid Contractions on Branciari Type Distance Spaces," Mathematics, MDPI, vol. 7(10), pages 1-11, October.

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