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The existence of best proximity points for multivalued non-self-mappings

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas volume 107, pages 319–325 (2013)Cite this article

Abstract

Let A, B be nonempty subsets of a metric space (X, d) and T : A → 2B be a multivalued non-self-mapping. The purpose of this paper is to establish some theorems on the existence of a point \({x^*\in A}\) , called best proximity point, which satisfies \({{\rm inf}\{d(x^*,y):y\in Tx^*\}=dist(A,B).}\) This will be done for contraction multivalued non-self-mappings in metric spaces, as well as for nonexpansive multivalued non-self-mappings in Banach spaces having appropriate geometric property.

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Authors and Affiliations

  1. Department of Mathematics, Imam Khomeini International University, 34149, Qazvin, Iran

    A. Abkar

  2. Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran

    M. Gabeleh

Authors
  1. A. Abkar
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  2. M. Gabeleh
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Correspondence to M. Gabeleh.

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Abkar, A., Gabeleh, M. The existence of best proximity points for multivalued non-self-mappings. RACSAM 107, 319–325 (2013). https://doi.org/10.1007/s13398-012-0074-6

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  • DOI: https://doi.org/10.1007/s13398-012-0074-6

Keywords

  • Contraction mapping
  • Nonexpansive mapping
  • Best proximity point
  • Fixed point

Mathematics Subject Classification (2000)

  • 47H10
  • 47H09