New results for the best proximity pair in cone Riesz space

Document Type : Research Paper


1 Computer Geometry and Dynamical Systems Laboratory, Yazd University, Yazd, Iran

2 Faculty of Mathematics, Yazd University, Yazd, Iran

3 Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran


In this paper, the best proximity pair problem is considered with a cone metric.  the conditions for the existence and uniqueness of the best proximity pair problem is discussed by using interesting relationships in Riesz spaces. This problem is studied for $T$-absolutely direct sets. Also, given the conditions considered for this problem, it is shown for the cone cyclic contraction maps, the best proximity pair problem is uniquely solvable.


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Volume 13, Issue 2
July 2022
Pages 2037-2041
  • Receive Date: 03 April 2019
  • Revise Date: 28 April 2020
  • Accept Date: 08 May 2020