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Coincidence Point, Best Approximation, and Best Proximity Theorems for Condensing Set-Valued Maps in Hyperconvex Metric Spaces

Fixed Point Theory and Applications volume 2008, Article number: 543154 (2008) Cite this article

Abstract

In hyperconvex metric spaces, we first present a coincidence point theorem for condensing set-valued self-maps. Then we consider the best approximation problem and the best proximity problem for set-valued mappings that are condensing. As an application, we derive a coincidence point theorem for nonself-condensing set-valued maps.

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Authors and Affiliations

  1. Department of Mathematics, University of Shahrekord, Shahrekord, 88186-34141, Iran

    A. Amini-Harandi

  2. Department of Mathematics, Razi University, Kermanshah, 67149, Iran

    A. P. Farajzadeh

  3. Department of Mathematics, National University of Ireland, Galway, Ireland

    D. O'Regan

  4. Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL, 32901, USA

    R. P. Agarwal

Authors
  1. A. Amini-Harandi
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  2. A. P. Farajzadeh
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  3. D. O'Regan
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  4. R. P. Agarwal
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Correspondence to A. Amini-Harandi.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Amini-Harandi, A., Farajzadeh, A.P., O'Regan, D. et al. Coincidence Point, Best Approximation, and Best Proximity Theorems for Condensing Set-Valued Maps in Hyperconvex Metric Spaces. Fixed Point Theory Appl 2008, 543154 (2008). https://doi.org/10.1155/2008/543154

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  • DOI: https://doi.org/10.1155/2008/543154

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