Maximal elements and coincident points for couple-majorized mappings in product topological vector spaces (Q1909621)

Summary: By introducing a concept called `couple-majorized mapping' in product topological vector spaces we establish existence theorems of maximal elements for couple-majorized set-valued families with arbitrary index set. As applications, some component coincidence and fixed points theorems are given which could be regarded as product extension version of the Fan-Browder fixed point theorem and related coincidence theorems. Finally, a coincidence theorem is used to derive the Sion minimax inequality in the case of two functions.