Best proximity point results for MK-proximal contractions on ordered sets

We discuss the existence and uniqueness of solutions to the minimization problem min(x is an element of A) d(x, Tx), where A, B are nonempty subsets of a partially ordered set X endowed with a metric d, and T : A -> B is a non-self-mapping satisfying a proximal contraction of Meir-Keeler type (MK-proximal contraction). An iterative algorithm is also provided to approximate the optimal solution. As particular cases of our obtained results, various fixed point theorems on a metric space endowed with a partial order are deduced.