Convex selections of multifunctions and their applications

Optimization

Volumn 55, Issue 1-2, 2006, Pages 91-99

  Michta, Mariusz ^a   Motyl, Jerzy ^a  

^a UNIVERSITY OF ZIELONA GÓRA   (Poland)

Author keywords

Differential and stochastic inclusion; Legendre Fenchel transform; Upper separated multifunction

Indexed keywords

EID: 33646462885     PISSN: 02331934     EISSN: 10294945     Source Type: Journal    
DOI: 10.1080/02331930500530153     Document Type: Article

References (24)

1. Ahmed, N.U., 1988, Semigroup Theory with Applications to Systems and Control (London: J. Wiley and Sons Ltd.).
2. Ahmed, N.U., 1988, Existence of Optimal Relaxed Controls for Differential Inclusions on Banach Spaces. Lecture Notes in Pure and Applied Mathematics, Vol. 109 (New York: M. Dekker, Inc.), pp. 39-49.
3. Ahmed, N.U., 1994, Nonlinear stochastic differential inclusions on Banach spaces. Stochastic Analysis and Applications, 12(1), 1-10.
4. Ahmed, N.U., 1994, Optimal relaxed controls for nonlinear infinite dimensional stochastic differential inclusions. Optimal Control of Differential Equations, Notes in Pure and Appl. Math. Vol. 160 (New York: M. Dekker), pp. 1-19.
5. Ahmed, N.U., 2002, Optimal control of impulsive stochastic evolution inclusions. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 22(2), 155-184.
6. Ahmed, N.U. and Xiang, X., 2003, Differential inclusions on Banach spaces and their optimal control. Nonlinear Functional Analysis and Applications, 8(3), 461-488.
7. Ahmed, N.U. and Xiang, X., 2003, Optimal relaxed controls for differential inclusions on Banach spaces. Stochastic Analysis and Applications, 12(1), 1-10.
8. Aubin, J.P. and Cellina, A., 1984, Differential Inclusions (Noordhoff: Leyden).
9. Aubin, J.P. and Frankowska, H., 1990, Set-Valued Analysis (Boston-Basel-Berlin: Birkhauser).
10. Barbu, V., 1976, Nonlinear Semigroups and Differential Equations in Banach Spaces (Noordhoff: Leyden).
11. Baron, K., Matkowski, J. and Nikodem, K., 1994, A sandwich with convexity. Mathematica Pannonica, 5, Univ. Miskolc, Math. Inst., Hungary, 139-144.
12. Bharucha-Reid, A.T., 1972, Random Integral Equations, Mathematics in Science and Engineering 96 (New York: Acad. Press).
13. Deutsch, F. and Singer, I., 1993, On single-valuedness of convex set-valued maps. Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications, 1, 97-103.
14. Gihman, I.I. and Skorohod, A.V., 1979, The Theory of Stochastic Processes III (New York: Springer Verlag).
15. Hale, J., 1977, Theory of Functional Differential Equations (Berlin-Heidelberg-New York: Springer Verlag).
16. Hyers, D.H. and Ulam, S.M., 1952, Approximately convex functions. Proceedings of the American Mathematical Society, 3, 821-828.
17. Kisielewicz, M., 1991, Differential Inclusions and Optimal Control (Warszawa-Dordrecht: Kluwer Acad. Publ. and Polish Sci. Publ.).
18. Krylov, N.V., 1980, Controlled Diffusion Processes, Applications of Mathematics (New York-Berlin: Springer Verlag).
19. Nikodem, K. and Wa̧sowicz, S., 1995, A sandwich theorem and Hyers-Ulam stability of affinne functions. Aequationes Mathematicae, 49, 160-164.
20. Øksendal, B., 1998, Stochastic Differential Equations, an Introduction with Applications, 5th Edn (Berlin: Springer Verlag).
21. Phelps, R.R., 1989, Convex Functions, Monotone Operators and Differentiability (Berlin-Heidelberg-New York: Springer Verlag).
22. Rishel, R.W. and Fleming, W.H., 1975, Deterministic and Stochastic Optimal Control, Applications of Mathematics (Berlin-New York: Springer Verlag).
23. Rockafellar, R.T. and Wets, R.J-B., 1998, Variational Analysis (Berlin-Heidelberg-New York: Springer Verlag).
24. Tolstonogov, A.A., 1986, Differencialnye vklucenja v Banachovom prostranstve, Izdatelstvo Nauka, Sibirskoe Oldelene. Novosibirsk (in Russian).