The Best Proximity Pair Focusing on Monotonicity and T-Absolutely Direct Sets

In this article, we mostly pay attention to the existence and uniqueness of the best proximity pair for T-absolutely direct sets. This investigation is based on some interesting relations existing in Banach lattices, in which T:A + B is an arbitrary map. The current provides a new view of the best proximity pair in Banach lattices by introducing T-absolutely direct sets.