Nonlinear versions of a vector maximal principle

Some nonlinear extensions of the vector maximality statement established by Goepfert et al. A. Goepfert, C. Tammer, C. Z?linescu, On the vectorial Ekeland’s variational principle and minimal points in product spaces, Nonlinear Anal. 39 (2000) 909-922] are given. Basic instruments for these are the Brezis-Browder ordering principle H. Brezis, F.E. Browder, A general principle on ordered sets in nonlinear functional analysis, Adv. Math. 21 (1976) 355-364] and its logical equivalent in Turinici M. Turinici, Variational principles on semi-metric structures, Libertas Math. 20 (2000) 161-171].