Nonlinear Versions of a Vector Maximal Principle

Some nonlinear extensions of the vector maximality statement established by Goepfert, Tammer and Zalinescu [Nonl. Anal., 39 (2000), 909-922] are given. Basic instruments for these are the Brezis-Browder ordering principle [Advances Math., 21 (1976), 355-364] and a (pseudometric) version of it obtained in Turinici [Demonstr. Math., 22 (1989), 213-228].