Abstract
Based on our 2023 Metatheorem in Ordered Fixed Point Theory, we give very simple proofs of known fixed point theorems for various multimap classes on quasi-metric spaces. Such classes are represented by the Banach contractions, the Rus-Hicks-Rhoades maps, the Nadler multimaps, Covitz-Nadler multimaps, and others. Consequently, we obtain simple proofs of a large number of known theorems on extremal elements, fixed points, stationary points for several classes of maps or multimaps. Finally, we add some known theorems for which our Metatheorem does not work.
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