Research

Journal of Inequalities and Applications

, 2012:206

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

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

Abstract

In this paper, we first introduce the new notion of MT http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2012-206/MediaObjects/13660_2012_Article_307_IEq1_HTML.gif-cyclic contraction and establish some new existence and convergence theorems of iterates of best proximity points for MT http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2012-206/MediaObjects/13660_2012_Article_307_IEq1_HTML.gif-cyclic contractions. Some nontrivial examples illustrating our results are also given.

MSC:41A17, 47H09.

Keywords

cyclic map best proximity point MT http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2012-206/MediaObjects/13660_2012_Article_307_IEq1_HTML.gif-function ( R http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2012-206/MediaObjects/13660_2012_Article_307_IEq2_HTML.gif-function) MT http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2012-206/MediaObjects/13660_2012_Article_307_IEq1_HTML.gif-cyclic contraction