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Best Proximity Point Results for Some Contractive Mappings in Uniform Spaces

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  • Victoria Olisama
  • Johnson Olaleru
  • Hudson Akewe

Abstract

We introduce the concept of -distance (an analogue of -metric), -proximal contraction, and -proximal cyclic contraction for non-self-mappings in Hausdorff uniform spaces. We investigate the existence and uniqueness of best proximity points for these modified contractive mappings. The results obtained extended and generalised some fixed and best proximity points results in literature. Examples are given to validate the main results.

Suggested Citation

  • Victoria Olisama & Johnson Olaleru & Hudson Akewe, 2017. "Best Proximity Point Results for Some Contractive Mappings in Uniform Spaces," International Journal of Analysis, Hindawi, vol. 2017, pages 1-8, April.
    • Handle: RePEc:hin:ijanal:6173468
    DOI: 10.1155/2017/6173468
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    References listed on IDEAS

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    1. S. Sadiq Basha, 2011. "Best Proximity Points: Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 210-216, October.
    2. Ali Abkar & Moosa Gabeleh, 2013. "A Note on Some Best Proximity Point Theorems Proved under P -Property," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-3, November.
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    Cited by:

    1. Manuel De la Sen & Asier Ibeas, 2022. "On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples," Mathematics, MDPI, vol. 10(14), pages 1-29, July.

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