Exceptional family of elements and solvability of variational inequalities for mappings defined only on closed convex cones in Banach spaces

Journal of Mathematical Analysis and Applications

Volumn 310, Issue 1, 2005, Pages 254-261

  Li, Jinlu ^a   Whitaker, John ^a  

^a SHAWNEE STATE UNIVERSITY   (United States)

Author keywords

Exceptional family of elements; Fixed point; Generalized projection operator; Leray Schauder type alternative; Variational inequality

Indexed keywords

EID: 23844507126     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.02.006     Document Type: Article

References (21)

1. Ya. Alber Metric and generalized projection operators in Banach spaces: properties and applications in: A. Kartsatos (Eds) Theory and Applications of Nonlinear Operators of Monotonic and Accretive Type 1996 Dekker New York 15-50
2. Ya. Alber S. GuerreDelabriere Problems of fixed point theory in Hilbert and Banach spaces Funct. Differ. Equ. 2 1994 5-10
3. Ya. Alber S. GuerreDelabriere Principle of weakly contractive maps in Hilbert spaces Oper. Theory Adv. Appl. 98 1997 7-22
4. Ya. Alber S. GuerreDelabriere On the projection methods for fixed point problems Analysis 21 2001 17-39
5. Ya. Alber S. GuerreDelabriere L. Zalenko The principle of weakly contractive maps in metric spaces Comm. Appl. Nonlinear Anal. 5 1998 45-68
6. Ya. Alber A. Notik On some estimates for projection operator in Banach space Comm. Appl. Nonlinear Anal. 2 1995 47-56
7. Ya. Alber S. Reich An iterative method for solving a class of nonlinear operator equations in Banach spaces Panamerican Math. J. 4 1994 39-54
8. J.M. Borwein Generalized linear complementarity problems treated without fixed point theory J. Optim. Theory Appl. 43 1984 343-356
9. R.W. Cottle J.S. Pang R.E. Stone The Linear Complementarity Problems 1992 Academic Press New York
10. G. Isac Nonlinear complementarity problems and Galerkin method J. Math. Anal. Appl. 108 1985 563-574
11. G. Isac On some generalization of Karamardian's Theorem on the complementarity problems Boll. Un. Mat. Ital. (B) 7 1988 323-332
12. G. Isac Complementarity Problems Lecture Notes in Math. vol. 1528 1992 Springer-Verlag Berlin
13. G. Isac, Leray-Schauder type alternatives and the solvability of complementarity problems, preprint, 2001
14. G. Isac V.A. Bulavski V.V. Kalashnikov Exceptional families of elements, topological degree and complementarity problems J. Global Optim. 10 1997 207-225
15. G. Isac W.T. Obuchowska Functions without exceptional families of elements and complementarity problems J. Optim. Theory Appl. 99 1998 147-163
16. G. Isac Y.B. Zhao Exceptional families of elements solvability of variational inequalities for unbounded sets in infinite dimensional Hilbert spaces J. Math. Anal. Appl. 246 2000 544-556
17. G. Isac, J.L. Li, Exceptional families of elements solvability of variational inequalities in spaces, in preparation
18. S. Karamardian Generalized complementarity problems J. Optim. Theory Appl. 8 1971 161-168
19. L.J. Lipkin Weak continuity and compactness of nonlinear mappings Nonlinear Anal. 5 1981 1257-1263
20. H.H. Schaefer Topological Vector Spaces 1966 Macmillan New York
21. Y.B. Zhao G. Isac Quasi- p * maps, P(τ, α, β) -maps, exceptional families of elements and complementarity problems J. Optim. Theory Appl. 105 2000 213-231