Semifixed sets of maps in hyperspaces with application to set differential equations

Set-Valued Analysis

Volumn 14, Issue 3, 2006, Pages 263-272

  De Blasi, F S ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Compact convex set; Hukuhara's derivative; Hyperspace; Multifunction; Semifixed set; Set differential equation

Indexed keywords

EID: 33746134082     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11228-005-0011-3     Document Type: Article

References (16)

1. Artstein, Z.: A calculus for set-valued maps and set-valued evolution equations, Set-Valued Anal. 3 (1995), 213-261.
2. Brandão Lopes Pinto, A. J., de Blasi, F. S. and Iervolino, F.: Uniqueness and existence theorems for differential equations with compact convex valued solutions, Boll. Un. Mat, Ital. 3(4) (1970), 47-54.
3. de Blasi, F. S. and Georgiev, P. G.: Kakutani-Fan's fixed point theorem in hyperspaces, Tokyo J. Math. 24 (2001), 331-342.
4. de Blasi, F. S. and Iervolino, F.: Equazioni differenziali con soluzioni a valore compatto convesso, Boll. Un. Mat. Ital. 2(4) (1969), 491-501.
5. de Blasi, F. S. and Pianigiani, G.: Approximate selections in α-convex metric spaces and topological degree, Topol. Methods Nonlinear Anal. 24 (2004), 347-375.
6. Górniewicz, L.: Topological Fixed Point Theory of Multivalued Mappings, Kluwer, Dordrecht, 1999.
7. Hukuhara, M: Intégration des applications mesurables dont la valeur est un compact convexe, Funkc. Ekvac. 10 (1967), 205-223.
8. Hu, S. and Papageorgiou, N. S.: Handbook of Multivalued Analysis, Kluwer, Dordrecht, 1997.
9. Kisielewicz, M.: Description of a class of differential equations with set-valued solutions, Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Nat. 58(8) (1975), 158-162.
10. Lakshmikantham, V., Leela, S. and Vatsala, A. S.: Interconnection between set and fuzzy differential equations, Nonlinear Anal. 54 (2003), 351-360.
11. Lakshmikantham, V. and Tolstonogov, A. N.: Existence and interrelation between set and fuzzy differential equations, Nonlinear Anal. 55 (2003), 255-268.
12. Nadler, S. B.: Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475-488.
13. Plotnikov, A. V.: Averaging differential inclusions with the Hukuhara derivative, Ukrainian Math. J. 41 (1989), 112-115.
14. Plotnikov, A. V. and Tumbzukaki, A. V.: Integrodifferential inclusions with Hukuhara's derivative, Nelīnnī Koliv. 8 (2005), 80-88.
15. Plotnikov, V. A. and Melnik, T. A.: A generalization of a theorem of A.N. Tikhonov for quasidifferential equations, Differential Equations 33 (1997), 1036-1040.
16. Tolstonogov, A. N.: Differential Inclusions in a Banach Space, Kluwer, Dordrecht, 2000.