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New Fixed Point Tools in Non-metrizable Spaces

Abstract

The aim of this paper is to provide some sufficient conditions under which a self-mapping T defined on a non-empty set X endowed with some convergence property is a Picard operator. A relevant example showing that such a mapping T on a non-metrizable space is a Picard operator is given. Our results can be used to obtain some known fixed point theorems on generalized metric spaces.

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Acknowledgements

The authors want to thank the anonymous reviewer for the insightful reading the manuscript and many useful remarks which improved the final version of the article. Project financed from Lucian Blaga University of Sibiu Research Grants LBUS-IRG-2016-02.

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Correspondence to Dariusz Wardowski.

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Secelean, NA., Wardowski, D. New Fixed Point Tools in Non-metrizable Spaces. Results Math 72, 919–935 (2017). https://doi.org/10.1007/s00025-017-0688-2

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  • DOI: https://doi.org/10.1007/s00025-017-0688-2

Mathematics Subject Classification

  • 47H09
  • 47H10

Keywords

  • Fixed point
  • \(\rho \psi \)-contraction
  • \(\rho \)-space
  • Non-metrizable space
  • Picard operator