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Bull. Korean Math. Soc. 2014; 51(2): 437-442

Printed March 31, 2014

https://doi.org/10.4134/BKMS.2014.51.2.437

Copyright © The Korean Mathematical Society.

Local completeness, lower semi continuous from above functions and Ekeland's principle

Carlos Bosch and Ren\'{e} Leal

Instituto Tecnol\'{o}gico Aut\'{o}nomo de M\'{e}xico:, Instituto Tecnol\'{o}gico Aut\'{o}nomo de M\'{e}xico:

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In this paper we prove Ekeland's variational principle in the setting of locally complete spaces for lower semi continuous functions from above and bounded below. We use this theorem to prove Caristi's fixed point theorem in the same setting and also for lower semi continuous functions.

Keywords: locally complete spaces, lower semi-continuity from above, variational principle, fixed point, minimization, equilibrium

MSC numbers: 49J53, 47H10, 46N10

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