Brezis-Browder Principles and Applications

Turinici, Mihai

doi:10.1007/978-1-4419-0158-3_14

Cited by 1 publication

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“…But, all arguments appearing in this proof are sequential in nature; so, we may expect that Theorem 6 is deductible in the reduced system (ZF-AC+DC). It is our aim in the following to show that, ultimately, this is possible by the recursion to a certain "transitive" form of Brezis-Browder ordering principle [10] established in Turinici [56]. Further aspects occasioned by these developments are also discussed.…”

Section: Pasicki Approachmentioning

confidence: 95%

“…By the remarks above, we may ask whether these enter as well in this reduction scheme. It is our aim in the present exposition to show that the results in question are obtainable from certain "transitive" type ordering principles like in Turinici [56]; whence, they are deductible from (DC). Moreover, these results include both (EVP) and (BB); so, by the above, they are nothing else than equivalent versions of (EVP) or (BB).…”

Section: Introductionmentioning

confidence: 93%

“…Note that, a further extension of (BB-t) in terms of general (amorphous) relations is possible; see Turinici [56] for details.…”

Section: By This Very Argument (Bb) H) (Bb-t) the Reciprocal Inclusmentioning

confidence: 99%

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Maximal and Variational Principles in Vector Spaces

Turinici

2015

Computation, Cryptography, and Network Security

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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).

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Section: Pasicki Approachmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 93%