The primary aim of this article is to resolve a global optimization problem in the setting of a partially ordered set that is equipped with a metric. Indeed, given non-empty subsets A and B of a partially ordered set that is endowed with a metric, and a non-self mapping <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${S : A \longrightarrow...</equationsource></inlineequation>