Some Results for Best Proximity Pair on Banach Lattices

Ali Asghar Sarvari, Hamid Mazaheri tehrani, Hamid Reza Khademzadeh

Abstract

As we know, most of the metric spaces we face in analysis havingnatural order that with this order become a lattice. In theorems related tothe best proximity pair on metric spaces, it doesn't use this useful tools. Inthis article we have used this natural order, and we proved the theorems onexistence and uniqueness of the best proximity pair on Banach lattices.