JOURNAL BROWSE
Search
Advanced SearchSearch Tips
LOCAL COMPLETENESS, LOWER SEMI CONTINUOUS FROM ABOVE FUNCTIONS AND EKELAND'S PRINCIPLE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
LOCAL COMPLETENESS, LOWER SEMI CONTINUOUS FROM ABOVE FUNCTIONS AND EKELAND'S PRINCIPLE
Bosch, Carlos; Leal, Rene;
  PDF(new window)
 Abstract
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;
 Language
English
 Cited by
 References
1.
S. Al-Homidan, Q. H. Ansari, and J.-C. Yao, Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory, Nonlinear Anal. 69 (2008), no. 1, 126-139. crossref(new window)

2.
M. Bianchi, G. Kassey, and R. Pini, Existence of equilibria via Ekeland's principle, J. Math. Anal. Appl. 284 (2003), 690-697. crossref(new window)

3.
C. Bosch, A. Garcia, and C. L. Garcia, An extension of Ekeland's variational principle to locally complete spaces, J. Math. Anal. Appl. 328 (2007), 106-108. crossref(new window)

4.
C. Bosch, A. Garcia, C. Gomez-Wulschner, and S. Hernandez-Linares, Equivalents to Ekeland's variational principle in locally complete spaces, Sci. Math. Japn. 72 (2010), no. 3, 283-287.

5.
Y. Chen, Y. J. Cho, and L. Yang, Note on the results with lower semi-continuity, Bull. Korean Math. Soc. 39 (2002), no. 4, 535-541. crossref(new window)

6.
I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324-353. crossref(new window)

7.
J. X. Fang, The variational principle and fixed point theorems in certain topological spaces, J. Math. Anal. Appl. 202 (1996), 398-412. crossref(new window)

8.
A. H. Hamel, Phelp's lemma, Danes'drop theorem and Ekeland's principle in locally convex spaces, Proc. Amer. Math. Soc. 131 (2003), no. 10, 3025-3038. crossref(new window)

9.
A. H. Hamel, Equivalents to Ekeland's variational principle in uniform spaces, Nonlinear Anal. 62 (2005), no. 5, 913-924. crossref(new window)

10.
H. Jarchow, Locally Convex Spaces, B. G. Teubner, Stuttgart, 1981.

11.
P. Perez-Carreras and J. Bonet, Barrelled Locally Convex Spaces, North-Holland, Amsterdam, 1987.

12.
J. H. Qiu, Local completeness and drop theorem, J. Math. Anal. Appl. 266 (2002), no. 2, 288-297. crossref(new window)

13.
J. H. Qiu, Ekeland's variational principle in locally complete spaces, Math. Nachr. 257 (2003), 55-58. crossref(new window)

14.
J. H. Qiu, Local completeness, drop theorem and Ekeland's variational principle, J. Math. Anal. Appl. 311 (2005), no. 1, 23-39. crossref(new window)