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New Approaches to Fixed Point Results on G-Metric Spaces

In: Fixed Point Theory in Metric Type Spaces

Author

Listed:
  • Ravi P. Agarwal

    (Texas A&M University-Kingsville, Department of Mathematics)

  • Erdal Karapınar

    (Atilim University, Department of Mathematics)

  • Donal O’Regan

    (National University of Ireland)

  • Antonio Francisco Roldán-López-de-Hierro

    (University of Granada, Department of Quantitative Methods for Economics and Business)

Abstract

Recently, Samet et al. [184], and Jleli and Samet [97], observed that some fixed point theorems in the context of G-metric space in the literature can be concluded from existence results in the setting of quasi-metric spaces. In fact, if the contractivity condition of the fixed point theorem on a G-metric space can be reduced to two variables instead of there variables, then one can construct an equivalent fixed point theorem in the setup of usual metric spaces. More precisely, in [97, 184], the authors noticed that q(x, y) = G(x, y, y) forms a quasi-metric.

Suggested Citation

  • Ravi P. Agarwal & Erdal Karapınar & Donal O’Regan & Antonio Francisco Roldán-López-de-Hierro, 2015. "New Approaches to Fixed Point Results on G-Metric Spaces," Springer Books, in: Fixed Point Theory in Metric Type Spaces, edition 1, chapter 0, pages 199-217, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-24082-4_8
    DOI: 10.1007/978-3-319-24082-4_8
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