Existence and convergence of best proximity points in \(\mathrm{{CAT}}_\mathrm{{p}}(0)\) spaces

Abstract

In this work, we study existence and convergence of best proximity points of a cyclic contraction mapping in a complete \(\mathrm{{CAT}}_\mathrm{{p}}(0)\) metric space, with \(p \ge 2\). The case of coupled best proximity points of a pair of cyclic contraction mappings is also discussed. As an application, we provide sufficient conditions to obtain an extension of the Banach Contraction Principle for coupled fixed points.

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Correspondence to S. Shukri.

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Shukri, S. Existence and convergence of best proximity points in \(\mathrm{{CAT}}_\mathrm{{p}}(0)\) spaces. J. Fixed Point Theory Appl. 22, 48 (2020). https://doi.org/10.1007/s11784-020-00785-6

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Keywords

  • Best proximity points
  • coupled best proximity points
  • fixed points
  • coupled fixed points
  • \(\mathrm{{CAT}}_\mathrm{{p}}(0)\) spaces
  • contraction mappings
  • cyclic contraction mappings

Mathematics Subject Classification

  • Primary 47H10
  • 54H25
  • Secondary 47H09
  • 46C20