Recently, we improved our long-standing Metatheorem in Fixed Point Theory. In this paper, as its applications, some well-known order-theoretic fixed point theorems are equivalently formulated as existence theorems on maximal elements, common fixed points, common stationary points, and others. Such theorems are the ones due to Banach, Nadler, Browder–Göhde–Kirk, Caristi–Kirk, Caristi, Brøndsted, and possibly many others.