Journal of Inequalities and Applications

, 2012:206

First online:

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Nonlinear conditions for the existence of best proximity points

  • Wei-Shih DuAffiliated withDepartment of Mathematics, National Kaohsiung Normal University Email author 
  • , Hossein LakzianAffiliated withDepartment of Mathematics, Payame Noor University


In this paper, we first introduce the new notion of -cyclic contraction and establish some new existence and convergence theorems of iterates of best proximity points for -cyclic contractions. Some nontrivial examples illustrating our results are also given.

MSC: 41A17, 47H09.


cyclic map best proximity point -function ( -function) -cyclic contraction