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. zălinescu, 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].