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Some Variational Results Using Generalizations of Sequential Lower Semicontinuity

Abstract

Kirk and Saliga and then Chen et al. introduced lower semicontinuity from above, a generalization of sequential lower semicontinuity, and they showed that well-known results, such as Ekeland's variational principle and Caristi's fixed point theorem, remain still true under lower semicontinuity from above. In a previous paper we introduced a new concept that generalizes lower semicontinuity from above. In the present one we continue such study, also introducing other two new generalizations of lower semicontinuity from above; we study such extensions, compare each other five concepts (sequential lower semicontinuity, lower semicontinuity from above, the one by us previously introduced, and the two here defined) and, in particular, we show that the above quoted well-known results remain still true under one of our such generalizations.

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Correspondence to Ada Bottaro Aruffo.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Bottaro Aruffo, A., Bottaro, G. Some Variational Results Using Generalizations of Sequential Lower Semicontinuity. Fixed Point Theory Appl 2010, 323487 (2010). https://doi.org/10.1155/2010/323487

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Keywords

  • Variational Result
  • Variational Principle
  • Point Theorem
  • Differential Geometry
  • Fixed Point Theorem