On Best Proximity Point Theorems without Ordering

الملخص EN

Recently, Basha (2013) addressed a problem that amalgamates approximation and optimization in the setting of a partially ordered set that is endowed with a metric.

He assumed that if A and B are nonvoid subsets of a partially ordered set that is equipped with a metric and S is a non-self-mapping from A to B , then the mapping S has an optimal approximate solution, called a best proximity point of the mapping S , to the operator equation S x = x , when S is a continuous, proximally monotone, ordered proximal contraction.

In this note, we are going to obtain his results by omitting ordering, proximal monotonicity, and ordered proximal contraction on S .