On the sum of monotone operators

Michigan Mathematical Journal

Volumn 43, Issue 2, 1996, Pages 273-289

  Chu, Liang Ju ^a  

^a NATIONAL TAIWAN NORMAL UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0006562511     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1029005463     Document Type: Article

References (28)

1. E. Asplund, Averaged norms, Israel J. Math. 5 (1967), 227-233.
2. _, Positivity of duality mappings, Bull. Amer. Math. Soc. 73 (1967), 200-203.
3. H. Brézis, Opérateurs maximaux monotones et seim-groupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam, 1973.
4. H. Brézis and A. Haraux, Image d'une somme d'opérateurs monotones et applications, Israel J. Math. 23 (1976), 165-185.
5. F. E. Browder, Nonlinear maximal monotone operators in Banach space, Math. Ann. 175 (1968), 89-113.
6. _, Coincidence theorems, minimax theorems and variational inequalities, Conference in modern analysis and probability (New Haven, CT, 1982), pp. 67-80, Amer. Math. Soc., Providence, RI, 1984.
7. L. J. Chu, Quasi-variational inequalities with acyclic multifunctions in locally convex spaces (to appear).
8. F. H. Clarke, Optimization and nonsmooth analysis, Centre de Recherches Mathématiques Université de Montréal, 1989.
9. D. F. Cudia, The geometry of Banach spaces: smoothness, Trans. Amer. Math. Soc. 110 (1964), 284-314.
10. S. C. Dafermos and S. C. McKelvey, Partitionable variational inequalities with applications to network and economic equilibria, J. Optim. Theory Appl. 73 (1992), 243-268.
11. S. C. Dafermos and A. Nagurney, Stability and sensitivity analysis for the general network equilibrium-travel choice model, 9th international symposium on transportation and traffic theory, pp. 217-231, VNU Press, Utrecht, Holland, 1984.
12. G. Isac, Complementarity problems, Lecture Notes in Math., 1528, Springer, New York, 1992.
13. J. F. McClendon, Minimax and variational inequalities for compact spaces, Proc. Amer. Math. Soc. 89 (1983), 717-721.
14. L. McLinden, Stable monotone variational inequalities, Math. Programming 48 (1990), 303-338.
15. Minty, G. J., On the maximal domain of a "monotone" function, Michigan Math. J. 8 (1961), 135-137.
16. _, On the monotonicity of the gradient of a convex function, Pacific J. Math. 14 (1964), 243-247.
17. J. J. Moreau, Proximité et dualité dans un espace hilbertien, Bull. Soc. Math. France 93 (1965), 273-299.
18. _, Fonctionelles convexes, mimeographed lecture notes, Collège de France.
19. R. R. Phelps, Convex functions, monotone operators, and differentiability, Lecture Notes in Math., 1364, Springer, New York, 1989.
20. R. T. Rockafellar, Characterization of the subdifferentials of convex functions, Pacific J. Math. 17 (1966), 497-510.
21. _, Convex functions, monotone operators and variational inequalities, Theory and applications of monotone operators (Proc. NATO Advanced Study Inst., Venice, 1968), Edizioni "Oderisi," pp. 35-60, Gubbio, 1969.
22. _, Convex analysis, Princeton Univ. Press, Princeton, NJ, 1970.
23. _, On the maximal monotonicity of subdifferential mappings, Pacific J. Math. 33 (1970), 209-216.
24. _, On the maximally of sums of nonlinear monotone operators, Trans. Amer. Math. Soc. 149 (1970), 75-88.
25. _, On the virtual convexity of the domain and range of a nonlinear maximal monotone operator, Math. Ann. 185 (1970), 81-90.
26. W. Rudin, Functional analysis, 2nd ed., McGraw-Hill, New York, 1991.
27. R. L. Torbin, Sensitivity analysis for variational inequalities, J. Optim. Theory Appl. 48 (1986), 191-209.
28. S. Troyanski, On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math. 37 (1971), 173-180.