Maximal and Variational Principles in Vector Spaces

Abstract

In Sect. 1, a separable type extension of Ekeland's variational principle (J Math Anal Appl 47:324-353, 1974) is given, in the realm of ordered convergence spaces. The connections with a related statement in Khanh (Bull Acad Pol Sci (Math) 37: [33][34][35][36][37][38][39] 1989) are then discussed. In Sect. 2, the Brezis-Browder ordering principle (Adv Math 21:355-364, 1976) is used to establish a lot of maximality results in triangular structures due to Pasicki (Nonlinear Anal 74:5678-5684, 2011). Finally, in Sect. 3, some technical aspects of the variational principle due to Bao and Mordukhovich (Control Cyb 36:531-562, 2007) are being analyzed. Further, an extension of this result is proposed, by means of a pseudometric maximal principle in Turinici (Note Mat 28:33-41, 2008).