Fixed-point theorems for discontinuous multivalued operators on ordered spaces with applications

Computers and Mathematics with Applications

Volumn 51, Issue 3-4, 2006, Pages 589-604

  Dhage, B C ^a  

^a Kasubai   (India)

Author keywords

Fixed point theorem; Functional differential inclusion

Indexed keywords

MANY VALUED LOGICS; NUMERICAL METHODS; PHASE SPACE METHODS; PROBLEM SOLVING; THEOREM PROVING;

FIXED-POINT THEOREM; FUNCTIONAL DIFFERENTIAL INCLUSION; MONOTONICITY CONDITIONS; MULTIVALUED OPERATORS;

MATHEMATICAL OPERATORS;

EID: 33747433807     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2005.07.017     Document Type: Article

References (22)

1. Dhage B.C. A lattice fixed-point theorem for multivalued mappings and applications. Chinese Journal of Math. 19 (1991) 11-22
2. Dhage B.C., and O'Regan D. A lattice fixed-point theorem and multivalued differential equations. Functional Dif. Equations 9 (2002) 109-115
3. Amann H. Order structures and fixed points. ATTI 20, Sem. Anal. Punz. Appl. (1977)
4. Heikkila S., and Lakshmikantham V. Monotone Iterative Technique for Nonlinear Discontinues Differential Equations (1994), Marcel Dekker Inc., New York
5. Agarwal R.P., Dhage B.C., and O'Regan D. The method of upper and lower solution for differential inclusions via a lattice fixed-point theorem. Dynamic Systems and Appl. 12 (2003) 1-7
6. Heikkila S., and Hu S. On fixed points of multi-functions in ordered spaces. Appl. Anal. 53 (1993) 115-127
7. Dhage B.C. Some algebraic fixed-point theorems for multivalued operators with applications. Diss. Math. Differential Inclusions, Control & Optim. 26 (2006)
8. Guo D., and Lakshmikanthm V. Nonlinear Problems in Abstract Cones (1988), Academic Press, New York
9. Dhage B.C. A fixed-point theorem for multivalued mappings in ordered Banach spaces with applications. PanAmer. Math. Journal 1 (2005) 15-34
10. Dhage B.C. A functional integral inclusion involving discontinuities. Fixed Point Theory 5 1 (2004) 53-64
11. Dhage B.C. On some variants of Schauder's fixed point principle and applications to nonlinear integral equations. J. Math. Phy. Sci. 25 (1988) 603-611
12. Dhage B.C. Fixed point theorems in ordered Banach algebras and applications. PanAmer. Math. Journal 9 4 (1999) 93-102
13. Dhage B.C. Multi-valued operators and fixed-point theorems in Banach algebras I. Taiwanese Journal Math 6 (2006)
14. Halidias N., and Papageorgiou N. Second order multivalued boundary value problems. Arch. Math. (Brno) 34 (1988) 267-284
15. Benchohra M., and Ntouyas S.K. On second order differential inclusions with periodic boundary conditions. Acta Mathematica Univ. Comenianea LXIX (2000) 173-181
16. Nieto J.J. Nonlinear second order periodic boundary value problems. J. Math. Anal. Appl. 130 (1988) 22-29
17. Lasota A., and Opial Z. An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phy. 13 (1965) 781-786
18. Aubin J., and Cellina A. Differential Inclusions (1984), Springer-Verlag, New York
19. Deimling K. Multi-valued Differential Equations (1998), De Gruyter, New York
20. Hu S., and Papageorgiou N.S. Handbook of Multivalued Analysis, Volume I: Theory (1997), Kluwer Academic Publishers, Berlin
21. Krasnoselskii M.A. Topological Methods in The Theory of Nonlinear Integral Equations (1964), Pergamon Press, Dordrechet
22. Dhage B.C. Monotone method for discontinuous differential inclusions. Math. Sci. Res. Journal 8 3 (2004) 104-113