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Last remarks on G-metric spaces and related fixed point theorems

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this report, we present some new fixed points theorems in the context of quasi-metric spaces that can be particularized in a wide range of different frameworks (metric spaces, partially ordered metric spaces, G-metric spaces, etc.). Our contractivity conditions involve different classes of functions and we study the case in which they only depend on a unique variable. Furthermore, we do not only introduce new contractivity conditions, but also expansivity conditions. As a consequence of our results, we announce that many fixed point results in G-metric spaces can be derived from the existing results if all arguments are not distinct.

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Acknowledgments

We are very thankful to the editor and to the anonymous reviewers for their careful reading of our manuscript and for their constructive reports, which have been very useful to improve the paper. The third author is grateful to the Department of Quantitative Methods for Economics and Business of the University of Granada (Spain). This manuscript has been partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE.

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Authors and Affiliations

  1. Department of Mathematics, Rhode Hall 217B, MSC 172 Texas A& M University-Kingsville, Kingsville, TX, 78363-8202, USA

    Ravi P. Agarwal

  2. Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Ravi P. Agarwal & Erdal Karapınar

  3. Atilim University, 06836, Incek, Ankara, Turkey

    Erdal Karapınar

  4. Department of Quantitative Methods for Economics and Business, University of Granada, Granada, Spain

    Antonio Francisco Roldán López de Hierro

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  1. Ravi P. Agarwal
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  2. Erdal Karapınar
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  3. Antonio Francisco Roldán López de Hierro
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Correspondence to Antonio Francisco Roldán López de Hierro.

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Agarwal, R.P., Karapınar, E. & Roldán López de Hierro, A.F. Last remarks on G-metric spaces and related fixed point theorems. RACSAM 110, 433–456 (2016). https://doi.org/10.1007/s13398-015-0242-6

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  • DOI: https://doi.org/10.1007/s13398-015-0242-6

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