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On Fixed and Best Proximity Points of Cyclic C-contractions in Probabilistic Complete Metric and Banach Spaces

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Abstract

This paper investigates some properties of boundedness and convergence of distances of \(p\)- cyclic \(C\)-quasi contractions and \(C\)-contractions in probabilistic complete metric spaces and uniformly convex Banach spaces as well as the existence and uniqueness of fixed points and best proximity points.

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Acknowledgments

The author is grateful to the Spanish Government for its support of this research with Grant DPI2012-30651, and to the Basque Government for its support of this research trough Grants IT378-10 and SAIOTEK S-PE12UN015. He is also grateful to the University of Basque Country for its financial support through Grant UFI 2011/07. Finally, the author thanks the reviewers for their useful suggestions.

Conflict of interest

The author declares that he has no competing interests.

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Authors and Affiliations

  1. Faculty of Science and Technology, Institute of Research and Development of Processes IIDP, University of the Basque Country, de Bilbao, Barrio Sarriena, PO Box 644, Leioa, 48940, Bizkaia, Spain

    M. De la Sen

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  1. M. De la Sen
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Correspondence to M. De la Sen.

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Communicated by Mohammad Sal Moslehian.

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De la Sen, M. On Fixed and Best Proximity Points of Cyclic C-contractions in Probabilistic Complete Metric and Banach Spaces. Bull. Malays. Math. Sci. Soc. 40, 1321–1340 (2017). https://doi.org/10.1007/s40840-015-0112-6

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  • DOI: https://doi.org/10.1007/s40840-015-0112-6

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