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Sequential Maximality Principles

In: Mathematics Without Boundaries

Author

Listed:
  • Mihai Turinici

    (“A. I. Cuza” University, “A. Myller” Mathematical Seminar)

Abstract

In Sect. 1, we show that all variational results deductible from the Bernays–Tarski Dependent Choices Principle and including Ekeland’s variational statement (J Math Anal Appl 47:324–353, 1974) are equivalent to each other. Moreover, in Sect. 2, one establishes that such a conclusion comprises as well the “asymptotic” versions of the Brezis-Browder ordering principle (Adv Math 21:355–364, 1976). The objective of Sect. 3 is to emphasize that the vector variational principles in Goepfert et al. (Nonlinear Anal 39:909–922, 2000) are obtainable from their scalar versions. Finally, in Sect. 4, we stress that the quasiorder version of the “smooth” variational principle in Borwein and Preiss (Trans Am Math Soc 303:517–527, 1987) is also entering in the logical segment we just described.

Suggested Citation

  • Mihai Turinici, 2014. "Sequential Maximality Principles," Springer Books, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Mathematics Without Boundaries, edition 127, pages 515-548, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-1106-6_20
    DOI: 10.1007/978-1-4939-1106-6_20
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