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\(\varphi \)-Best proximity point theorems and applications to variational inequality problems

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Abstract

The main concern of this study is to introduce the notion of \(\varphi \)-best proximity points and establish the existence and uniqueness of \(\varphi \)-best proximity point for non-self mappings satisfying \((F,\varphi )\)-proximal and \((F,\varphi )\)-weak proximal contraction conditions in the context of complete metric spaces. Some examples are supplied to support the usability of our results. As applications of the obtained results, some new best proximity point results in partial metric spaces are presented. Furthermore, sufficient conditions to ensure the existence of a unique solution for a variational inequality problem are also discussed.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts, Muş Alparslan University, 49100, Muş, Turkey

    Hüseyin Işık

  2. Department of Mathematics, Faculty of Science and Arts, University of Giresun, Gazipaşa, Giresun, Turkey

    M. Sangurlu Sezen

  3. Department of Mathematics and Computer Sciences, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Calogero Vetro

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  1. Hüseyin Işık
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  2. M. Sangurlu Sezen
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  3. Calogero Vetro
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Correspondence to Hüseyin Işık.

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Işık, H., Sezen, M.S. & Vetro, C. \(\varphi \)-Best proximity point theorems and applications to variational inequality problems. J. Fixed Point Theory Appl. 19, 3177–3189 (2017). https://doi.org/10.1007/s11784-017-0479-0

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  • DOI: https://doi.org/10.1007/s11784-017-0479-0

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