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Best proximity points of non-self mappings

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  • Ali Abkar
  • Moosa Gabeleh

Abstract

Let A,B be nonempty subsets of a Banach space X and let T:A→B be a non-self mapping. Under appropriate conditions, we study the existence of solutions for the minimization problem min x∈A ∥x−Tx∥. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • Ali Abkar & Moosa Gabeleh, 2013. "Best proximity points of non-self mappings," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 287-295, July.
    • Handle: RePEc:spr:topjnl:v:21:y:2013:i:2:p:287-295
    DOI: 10.1007/s11750-012-0255-7
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    References listed on IDEAS

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    1. Xiaolong Qin & Shin Kang & Yeol Cho, 2010. "Approximating zeros of monotone operators by proximal point algorithms," Journal of Global Optimization, Springer, vol. 46(1), pages 75-87, January.
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    Cited by:

    1. G. Poonguzali & V. Pragadeeswarar & Manuel De la Sen, 2023. "Existence of Best Proximity Point in O -CompleteMetric Spaces," Mathematics, MDPI, vol. 11(16), pages 1-9, August.
    2. 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.
    3. Mustafa Aslantas, 2022. "Finding a Solution to an Optimization Problem and an Application," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 121-141, July.

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