Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions
Dhage, Bapurao Chandra
Archivum Mathematicum, Tome 043 (2007), p. 265-284 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

In this paper, some hybrid fixed point theorems for the right monotone increasing multi-valued mappings in ordered Banach spaces are proved via measure of noncompactness and they are further applied to the neutral functional nonconvex differential inclusions involving discontinuous multi-functions for proving the existence results under mixed Lipschitz, compactness and right monotonicity conditions. Our results improve the multi-valued hybrid fixed point theorems of Dhage (Dhage, B. C., A fixed point theorem for multivalued mappings on ordered Banach spaces with applications I, Nonlinear Anal. Forum 10 (2005), 105–126.) under weaker convexity conditions.

Publié le : 2007-01-01
Classification:  34A60,  34K40,  47A25,  47H10,  47N20 
@article{108071,
     author = {Bapurao Chandra Dhage},
     title = {Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions},
     journal = {Archivum Mathematicum},
     volume = {043},
     year = {2007},
     pages = {265-284},
     zbl = {1164.47056},
     mrnumber = {2378527},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108071}
}

Dhage, Bapurao Chandra. Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions. Archivum Mathematicum, Tome 043 (2007) pp. 265-284. http://gdmltest.u-ga.fr/item/108071/

Agarwal R. P.; Dhage B. C.; O’Regan D. The method of upper and lower solution for differential inclusions via a lattice fixed point theorem, Dynamic Systems Appl. 12 (2003), 1–7. | MR 1989018

Akhmerov P. P.; Kamenskii M. I.; Potapov A. S.; Sadovskii B. N. Measures of Noncompactness and Condensing Operators, Birkhäuser 1992. (1992) | MR 1153247

Andres J.; Górniewicz L. Topological Fixed Point Principles for Boundary Value Problems, Kluwer, 2003. | MR 1998968

Banas J.; Lecko M. Fixed points of the product of operators in Banach algebras, PanAmer. Math. J. 12 (2002), 101–109. | MR 1895774

Covitz H.; Nadler S. B., Jr. Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5–11. (1970) | MR 0263062

Deimling K. Multi-valued Differential Equations, De Gruyter, Berlin 1998. (1998)

Dhage B. C. Multi-valued operators and fixed point theorems in Banach algebras I, Taiwanese J. Math. 10 (4), (2006), 1025–1045. | MR 2229639 | Zbl 1144.47321

Dhage B. C. Multi-valued mappings and fixed points I, Nonlinear Funct. Anal. Appl. 10 (3), (2005), 359–378. | MR 2194603 | Zbl 1100.47040

Dhage B. C. Hybrid fixed point theory for strictly monotone increasing multi-valued mappings with applications, Comput. Math. Appl. 53 (2007), 803–824. | MR 2327635 | Zbl 1144.47041

Dhage B. C. A fixed point theorem for multivalued mappings on ordered Banach spaces with applications I, Nonlinear Anal. Forum 10 (2005), 105–126. | MR 2162344

Dhage B. C. A general multi-valued hybrid fixed point theorem and perturbed differential inclusions, Nonlinear Anal. 64 (2006), 2747–2772. | MR 2218544 | Zbl 1100.47045

Dhage B. C. Some algebraic fixed point theorems for multi-valued operators with applications, DISC. Math. Differential inclusions, Control & Optimization 26 (2006), 5–55. | MR 2330779

Dhage B. C.; Ntouyas S. K. Existence results for neutral functional differential inclusions, Fixed Point Theory 5 (2005), 235–248. | MR 2117335 | Zbl 1080.34063

Dajun Guo; Lakshmikanthm V. Nonlinear Problems in Abstract Cones, Academic Press, New York–London, 1988. (1988)

Hale J. K. Theory of Functional Differential Equations, Springer, New York 1977. (1977) | MR 0508721 | Zbl 0352.34001

Heikkilä S.; Lakshmikantham V. Monotone Iterative Technique for Nonlinear Discontinues Differential Equations, Marcel Dekker Inc., New York, 1994. (1994) | MR 1280028

Heikkilä S.; Hu S. On fixed points of multi-functions in ordered spaces, Appl. Anal. 53 (1993), 115–127. (1993)

Hu S.; Papageorgiou N. S., Handbook of Multivalued Analysis, Vol. I: Theory, Kluwer Academic Publishers, Dordrechet–Boston–London 1997. (1997) | MR 1485775

Lasota A.; Opial Z. An application of the Kakutani- Ky Fan theorem in the theory of ordinary differential equations, Bull. Polish Acad. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781–786. (1965) | MR 0196178 | Zbl 0151.10703

Ntouyas S. K. Initial and boundary value problems for functional differential equations via topological transversality method : A Survey, Bull. Greek Math. Soc. 40 (1998), 3–41. (1998) | MR 1671786

Petruşel A. Operatorial Inclusions, House of the Book of Science, Cluj-Napoca, 2002. | MR 1939244 | Zbl 1057.47004

Zeidler E. Nonlinear Functional Analysis and Its Applications: Part I, Springer Verlag, 1985. (1985) | MR 0768749