Implicit function theorems for m-accretive and locally accretive set-valued mappings

Nonlinear Analysis, Theory, Methods and Applications

Volumn 41, Issue 1, 2000, Pages 221-241

  Domokos, A ^a  

^a BABE BOLYAI UNIVERSITY   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; PERTURBATION TECHNIQUES; POLES AND ZEROS; PROBLEM SOLVING; THEOREM PROVING;

ACCRETIVE SET-VALUED MAPPINGS; DUALITY MAPPINGS; IMPLICIT FUNCTION THEOREMS;

NONLINEAR EQUATIONS;

EID: 0034230919     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00275-2     Document Type: Article

References (32)

1. W. Alt, I. Kolumban, Implicit function theorems for monotone mappings, Kybernetika Prague 29 (1993) 210-221.
2. J.P. Aubin, H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990.
3. V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Academiei and Noorghoff International Publishing, Bucharest-Leyden, 1976.
4. F.E. Browder, Nonlinear equations of evolution and nonlinear accretive operators in banach spaces, Bull. Amer. Math. Soc. 73 (1967) 867-874.
5. R.E. Bruck, On characterization of Hilbert space, Proc. Amer. Math. Soc. 43 (1974) 173-175.
6. B. Calvert, Maximal accretive is not m-accretive, Boll. Un. Ital. 6 (1970) 1042-1044.
7. A. Cernes, Ensembles maximaux accrétifs et m-accrétifs, Israel J. Math. 19 (1974) 335-348.
8. I. Cioranescu, Aplicaţii de Dualitate in Analiza Neliniara, Academiei, Bucuresti, 1974.
9. S. Dafermos, Sensitivity analysis in variational inequalities, Math. Oper. Res. 13 (1988) 421-433.
10. K. Deimling, Zeros of accretiv operators, Manuscripta Math. 13 (1974) 365-375.
11. K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
12. A. Domokos, Parametric monotone generalized equations in reflexive banach spaces, Math. Pannonica 8 (1997) 129-136.
13. A. Domokos, Perturbation Analysis of Monotone Generalized Equations, submitted.
14. A.L. Dontchev, W.W. Hager, Implicit functions, lipschitz maps and stability in optimization, Math. Oper. Res. 19 (1994) 753-768.
15. H. Gajewski, K. Gröger, K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleinchungen, Akademie-Verlag, Berlin, 1974.
16. A.G. Kartsatos, New results in the perturbation theory of maximal-monotone and m-accretive operators in banach spaces, Trans. Amer. Math. Soc. 348 (1996) 1663-1707.
17. W.A. Kirk, On local expansions and accretive mappings, Int. J. Math. 6 (1983) 419-429.
18. W.A. Kirk, R. Schöneberg, Zeros of m-accretive operators in banach spaces, Israel J. Math. 35 (1980) 1-8.
19. A. Kufner, O. John, S. Fucik, Function Spaces, Publishing House of the Czechoslovak Academy of Science, Prague, 1977.
20. C. Morales, Pseudo-contractive mappings and the Leray-Schauder boundary condition, Comment. Math. Univ. Carolinae 20 (1979) 745-757.
21. C. Morales, Existence theorems for demicontinuous accretive operators in banach spaces, Houston J. Math. 10 (1984) 535-543.
22. C. Morales, Surjectivity theorems for multivalued mappings of accretive type, Comment. Math. Univ. Carolinae 26 (1985) 397-413.
23. C. Morales, Zeros for strongly accretive set-valued mappings, Comment. Math. Univ. Carolinae 27 (1986) 455-469.
24. N.S. Papageorgiu, On evolution inclusions driven by m-accretive operators, PUMA 7 (1996) 139-163.
25. J. Prüß, A characterization of uniform-convexity and application to accretive operators, Hiroshima Math. J. 11 (1981) 229-234.
26. S. Reich, Extension problems for accretive sets in banach spaces, J. Funct. Anal. 26 (1977) 378-395.
27. S. Reich, R. Torrejon, Zeros of accretive operators, Comment. Math. Univ. Carolinae 21 (1980) 619-625.
28. S.M. Robinson, Strongly regular generalized equations, Math. Oper. Res. 5 (1980) 43-62.
29. S.M. Robinson, An implicit function theorem for a class of nonsmooth functions, Math. Oper. Res. 16 (1991) 292-309.
30. I. Vrabie, Compactness Methods for Nonlinear Evolutions, Wiley, New York, 1987.
31. N.D. Yen, Hölder continuity of solutions to a parametric variational inequality, Appl. Math. Optim. 31 (1995) 245-255.
32. E. Zeidler, Nonlinear Functional Analysis and its Applications, vol. II/b, Springer, Berlin, 1990.