We introduce generalized Frobenius–Perron operators associated with measurable transformations between two measurable spaces and study their basic properties. The new concept extends the well-known Frobenius–Perron operators from ergodic theory to a more general setting. We then discuss the optimal transport problem in terms of generalized Frobenius–Perron operators, providing a new perspective for their theoretical and numerical studies.
Zhu et al. (Wed,) studied this question.