Recessively compact sets: Properties and uses

Set-Valued Analysis

Volumn 10, Issue 1, 2002, Pages 15-35

  The Luc, Dinh ^a,b  

^a UNIVERSITY OF AVIGNON   (France)

^b INSTITUTE OF MATHEMATICS   (Viet Nam)

Author keywords

Closed image; Finite intersection property; Fixed point theorem; Periodic solution of a differential equation; Recessively compact set; Variational inequality

Indexed keywords

EID: 0041396856     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014458603461     Document Type: Article

References (29)

1. Agadi, A.: Cône asymptotes en analyse nonlinéaire, Thèse de doctorat, Université de Pau, 1995.
2. Attouch, H. and Brezis, H.: Duality for the sum of convex functions in general Banach spaces, In: J. A. Barroso (ed.), Aspects of Mathematics and its Applications, Elsevier, Amsterdam, 1986, pp. 125-133.
3. Aubin, J. P. and Ekeland, J.: Applied Nonlinear Analysis, Wiley, New York, 1984.
4. Aubin, J. P. and Frankowska, H.: Set Valued Analysis, Birkhauser, Basel, 1990.
5. Auslender, A.: Closedness criteria for the image of a closed set, Preprint, Université de Paris I, Laboraoire d'Econométrie de l'Ecole Polytechnique, 1995.
6. Baiocchi, C., Buttazzo, G., Gastaldi, F. and Tomarelli, F.: General existence theorems for unilateral problems in continuum mechanics, Arch. Rat. Mech. Anal. 100 (1988), 149-189.
7. Browder, F.: Periodic solution of nonlinear equation in infinite dimensional space, In: A. Aziz (ed.), Lecture Series in Differential Equation, Van Nostrand, New York, 1969, pp. 71-93.
8. Choquet, G.: Ensemble et cones convexes faiblement complets, C.R. Acad. Sci. Paris 254 (1962), 1908-1910.
9. Debreu, G.: Theory of Value, Yake Univ. Press, New Haven, 1975.
10. Dedieu, J. P.: Critères de fermeture pour l'image d'un fermé non convexe par une multiapplication, C.R. Acad. Sci. Paris 287 (1978), 501-503.
11. Dieudonné, J.: Sur la séparation des ensembles convexes, Math. Ann. 163 (1966), 1-3.
12. Fenchel, W.: Convex cones, sets and functions, Mimeographed lecture notes, Princeton Univ., Princeton, NJ, 1951.
13. Gwinner, J.: Closed images of convex multivalued mappings in linear topological spaces with applications, J. Math. Anal. Appl. 60 (1977), 75-86.
14. Hartman, G. J. and Stampacchia, G.: On some nonlinear elliptic differential equations, Acta Math. 115 (1966), 271-310.
15. Klee, V. L.: Asymptotics and projections of convex sets, Math. Scand. 8 (1960), 356-362.
16. Lassonde, L.: Minimax et points fixes: Théorèmes de base, Preprint, Université Blaise Pascal, 1992.
17. Luc, D. T.: Theory of Vector Optimization, Lecture Notes in Econ. and Math. Systems 319, Springer, New York, 1989.
18. Luc, D. T.: Recession cones and the domination property in vector optimization, Math. Programming 49 (1990), 113-122.
19. Luc, D. T.: Recession maps and applications, Optimization 27 (1993), 1-15.
20. Luc, D. T. and Penot, J. P.: Convergence of asymptotic directions, Trans. Amer Math. Soc. 353 (2001), 4095-4121.
21. Luc, D. T. and Volle, M.: Semicontinuity and exactness of nonconvex image functions, Preprint, Unviresité d'Avignon, 1995.
22. Rockafellar, R. T.: Convex Analysis, Princeton Univ. Press, Princeton, NJ, 1970.
23. Rockafellar, R. T. and Wets, R.: Variational Analysis, Springer, Berlin, 1998.
24. Steinitz, E.: Bedingt konvergente Reihen und konvexe Systeme I, II, III, J. Math. 143 (1913), 128-175; 144 (1914), 1-40; 146 (1916), 1-52.
25. Steinitz, E.: Bedingt konvergente Reihen und konvexe Systeme I, II, III, J. Math. 143 (1913), 128-175; 144 (1914), 1-40; 146 (1916), 1-52.
26. Steinitz, E.: Bedingt konvergente Reihen und konvexe Systeme I, II, III, J. Math. 143 (1913), 128-175; 144 (1914), 1-40; 146 (1916), 1-52.
27. Zalinescu, C.: Stability for a class of nonlinear optimization problems and applications, In: F. Clarke, V. F. Demyanov and F. Giannessi (eds), Nonsmooth Optimization and Related Topics, Plenum Press, New York, 1989, pp. 437-458.
28. Zalinescu, C.: Recession cones and asymptotically compact sets, J. Optim. Theory Appl. 77 (1993), 209-220.
29. Zeidler, E.: Nonlinear Functional Analysis and Its Applications, Part 1: Fixed-Point Theorems, Springer, New York, 1986.