ABSTRACT
Motivated by the Ekeland variational principle, we obtained a Metatheorem in 1985-87 stating that some well-known order theoretic fixed point theorems can be equivalently formulated to existence theorems on maximal elements, common fixed points, common stationary points, and others. Unknowing this, Fierro in 2017 obtained an extended version of our particular form of Metatheorem in 2000. In 2022, Boros, Iqbal, and Szaz claimed that an implication of Fierro's theorem is not adequate. In such situation, we returned to our Metatheorem in 2022 and established certain Foundations of Ordered Fixed Point Theory. The present chapter aims to introduce the claims of Fierro and Boros et al. with our 2023 version of Metatheorem and to resolve the conict.
