We introduce the new concepts of e -distance, e -type mapping with respect to some e -distance and S -complete quasimetric space, and prove minimization theorems, fixed point theorems, and variational principles on an S -complete quasimetric space. We also give some examples of quasimetrics, e -distances, and e -type mapping with respect to some e -distance. Our results extend, improve, and unify many known results due to Caristi, Ekeland, Ćirić, Kada-Suzuki-Takahashi, Ume, and others.