Equivalents to Ekeland's variational principle in uniform spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 62, Issue 5, 2005, Pages 913-924

  Hamel, Andreas H ^a  

^a NONE   (Brazil)

Author keywords

Ekeland's variational principle, Uniform spaces; Minimal element theorem

Indexed keywords

FUNCTIONS; LINEAR SYSTEMS; OPTIMIZATION; SET THEORY; THEOREM PROVING; TOPOLOGY;

EKELAND'S VARIATIONAL PRINCIPLE; MINIMAL ELEMENT THEOREM; TOPOLOGICAL LINEAR SPACES; UNIFORM SPACES;

VARIATIONAL TECHNIQUES;

EID: 21244448781     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.04.011     Document Type: Article

References (23)

1. A. Brønstedt On a lemma of Bishop and Phelps Pacific J. Math. 55 2 1974 335 341
2. J. Caristi Fixed Point Theorems for Mappings Satisfying Inwardness Conditions Trans. Amer. Math. Soc. 215 1976 241 251
3. I. Ekeland On the variational principle J. Math. Anal. Appl. 47 1974 324 353
4. J.-X. Fang The variational principle and fixed point theorems in certain topological spaces J. Math. Anal. Appl. 202 1996 398 412
5. C. Gerstewitz (Tammer) Nichtkonvexe Dualität in der Vektoroptimierung Wiss Z. TH Leuna-Merseburg 25 3 1983 357 364
6. C. Gerstewitz (Tammer), and E. Iwanow Dualität für nichtkonvexe Vektoroptimierungsprobleme Wiss. Z. TH Ilmenau 31 2 1985 61 81
7. C. Gerth (Tammer), and P. Weidner Nonconvex separation theorems and some applications in vector optimization JOTA 67 2 1990 297 320
8. A. Göpfert, C. Tammer, and C. Zǎlinescu On the vectorial Ekeland's variational principle and minimal points in product spaces Nonlinear Anal. 39 2000 909 922
9. A. Göpfert, H. Riahi, C. Tammer, C. Zǎlinescu, Variational methods in partially ordered spaces, CMS Books in Mathematics, vol. 17, Springer, New York, 2003.
10. A. Hamel Variational principles on metric and uniform spaces 2005 Habilitation Thesis Halle
11. A.H. Hamel, A. Löhne, Minimal set theorems, Report of the Institute of Optimization and Stochastics, Martin-Luther-University Halle-Wittenberg, Department of Mathematics and Computer Science, 2002, p. 11.
12. A. Hamel, A. Löhne, A Minimal Point Theorem in Uniform Spaces, in: R.P. Argaval, D. O'Regan, Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday, Kluwer Academic Publisher, vol. 1, 2003, pp. 577-593.
13. D.H. Hyers, G. Isac, and T.M. Rassias Topics in Nonlinear Analysis & Applications 1997 World Scientific Singapore
14. J.L. Kelly General Topology 1955 Springer New York
15. G. Köthe Topologische lineare Räume I 1966 Springer Berlin
16. N. Mizoguchi A generalization of Brønstedt's results and its applications Proc. Amer. Math. Soc. 108 3 1990 707 714
17. A.B. Nemeth A nonconvex vector minimization problem Nonlinear Anal. 10 1986 669 678
18. A.B. Nemeth Ekeland's variational principle in ordered Abelian groups Nonlinear Anal. Forum 6 2 2001 299 312
19. A.B. Nemeth, Regular Orderings and Existence of Minimum Points in Uniform Spaces and Topological Groups, Positivity, 2004.
20. W. Oettli, and M. Théra Equivalents of Ekeland's Principle Bull. Austral. Math. Soc. 48 1993 385 392
21. J.-P. Penot The Drop Theorem, the Petal Theorem and Ekeland's Variational Principle Nonlinear Anal. Theory, Methods Appl. 10 9 1986 813 822
22. W. Takahashi, Existence theorems generalizing fixed point theorems for multivalued mappings, in: J.-B. Baillon/M. Thera, Fixed Point Theory and Applications, Longman S&T, 1991, pp. 397-406.
23. P. Weidner, Ein Trennungskonzept und seine Anwendung auf Vektoroptimierungsverfahren, Habilitation Thesis, Halle, 1990.