# Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions

Archivum Mathematicum (2007)

- Volume: 043, Issue: 4, page 265-284
- ISSN: 0044-8753

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topDhage, Bapurao Chandra. "Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions." Archivum Mathematicum 043.4 (2007): 265-284. <http://eudml.org/doc/250172>.

@article{Dhage2007,

abstract = {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.},

author = {Dhage, Bapurao Chandra},

journal = {Archivum Mathematicum},

keywords = {ordered Banach space; hybrid fixed point theorem; neutral functional differential inclusion and existence theorem; ordered Banach space; hybrid fixed point theorem},

language = {eng},

number = {4},

pages = {265-284},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions},

url = {http://eudml.org/doc/250172},

volume = {043},

year = {2007},

}

TY - JOUR

AU - Dhage, Bapurao Chandra

TI - Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions

JO - Archivum Mathematicum

PY - 2007

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 043

IS - 4

SP - 265

EP - 284

AB - 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.

LA - eng

KW - ordered Banach space; hybrid fixed point theorem; neutral functional differential inclusion and existence theorem; ordered Banach space; hybrid fixed point theorem

UR - http://eudml.org/doc/250172

ER -

## References

top- 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. MR1989018
- Akhmerov P. P., Kamenskii M. I., Potapov A. S., Sadovskii B. N., Measures of Noncompactness and Condensing Operators, Birkhäuser 1992. (1992) MR1153247
- Andres J., Górniewicz L., Topological Fixed Point Principles for Boundary Value Problems, Kluwer, 2003. MR1998968
- Banas J., Lecko M., Fixed points of the product of operators in Banach algebras, PanAmer. Math. J. 12 (2002), 101–109. MR1895774
- Covitz H., Nadler S. B., Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5–11. (1970) MR0263062
- 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. Zbl1144.47321MR2229639
- Dhage B. C., Multi-valued mappings and fixed points I, Nonlinear Funct. Anal. Appl. 10 (3), (2005), 359–378. Zbl1100.47040MR2194603
- Dhage B. C., Hybrid fixed point theory for strictly monotone increasing multi-valued mappings with applications, Comput. Math. Appl. 53 (2007), 803–824. Zbl1144.47041MR2327635
- Dhage B. C., A fixed point theorem for multivalued mappings on ordered Banach spaces with applications I, Nonlinear Anal. Forum 10 (2005), 105–126. MR2162344
- Dhage B. C., A general multi-valued hybrid fixed point theorem and perturbed differential inclusions, Nonlinear Anal. 64 (2006), 2747–2772. Zbl1100.47045MR2218544
- Dhage B. C., Some algebraic fixed point theorems for multi-valued operators with applications, DISC. Math. Differential inclusions, Control & Optimization 26 (2006), 5–55. MR2330779
- Dhage B. C., Ntouyas S. K., Existence results for neutral functional differential inclusions, Fixed Point Theory 5 (2005), 235–248. Zbl1080.34063MR2117335
- 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) Zbl0352.34001MR0508721
- Heikkilä S., Lakshmikantham V., Monotone Iterative Technique for Nonlinear Discontinues Differential Equations, Marcel Dekker Inc., New York, 1994. (1994) MR1280028
- 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) MR1485775
- 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) Zbl0151.10703MR0196178
- 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) MR1671786
- Petruşel A., Operatorial Inclusions, House of the Book of Science, Cluj-Napoca, 2002. Zbl1057.47004MR1939244
- Zeidler E., Nonlinear Functional Analysis and Its Applications: Part I, Springer Verlag, 1985. (1985) MR0768749

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