Convex selections of multifunctions and their applications

References

• Ahmed , NU . 1988 . Semigroup Theory with Applications to Systems and Control , London : J. Wiley and Sons Ltd. .
   Google Scholar
• Ahmed , NU . 1988 . “ Existence of Optimal Relaxed Controls for Differential Inclusions on Banach Spaces ” . In Lecture Notes in Pure and Applied Mathematics , Vol. 109 , 39 – 49 . New York : M. Dekker, Inc. .
   Google Scholar
• Ahmed , NU . 1994 . Nonlinear stochastic differential inclusions on Banach spaces . Stochastic Analysis and Applications , 12 ( 1 ) : 1 – 10 .
   Web of Science ®Google Scholar
• Ahmed , NU . 1994 . “ Optimal relaxed controls for nonlinear infinite dimensional stochastic differential inclusions ” . In Optimal Control of Differential Equations , Vol. 160 , 1 – 19 . New York : M. Dekker . Notes in Pure and Appl. Math
   Google Scholar
• Ahmed , NU . 2002 . Optimal control of impulsive stochastic evolution inclusions . Discussiones Mathematicae. Differential Inclusions, Control and Optimization , 22 ( 2 ) : 155 – 184 .
   Google Scholar
• Ahmed , NU and Xiang , X . 2003 . Differential inclusions on Banach spaces and their optimal control . Nonlinear Functional Analysis and Applications , 8 ( 3 ) : 461 – 488 .
   Google Scholar
• Ahmed , NU and Xiang , X . 2003 . Optimal relaxed controls for differential inclusions on Banach spaces . Stochastic Analysis and Applications , 12 ( 1 ) : 1 – 10 .
   Web of Science ®Google Scholar
• Aubin , JP and Cellina , A . 1984 . Differential Inclusions , Noordhoff : Leyden .
   Google Scholar
• Aubin , JP and Frankowska , H . 1990 . Set-Valued Analysis , Boston–Basel–Berlin : Birkhauser .
   Google Scholar
• Barbu , V . 1976 . Nonlinear Semigroups and Differential Equations in Banach Spaces , Noordhoff : Leyden .
   Google Scholar
• Baron , K , Matkowski , J and Nikodem , K . 1994 . “ A sandwich with convexity ” . In Mathematica Pannonica , Vol. 5 , 139 – 144 . Hungary : Univ. Miskolc, Math. Inst .
   Google Scholar
• Bharucha-Reid , AT . 1972 . Random Integral Equations, Mathematics in Science and Engineering 96 , New York : Acad. Press .
   Google Scholar
• 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 .
   Google Scholar
• Gihman , II and Skorohod , AV . 1979 . The Theory of Stochastic Processes III , New York : Springer Verlag .
   Google Scholar
• Hale , J . 1977 . Theory of Functional Differential Equations , Berlin–Heidelberg–New York : Springer Verlag .
   Google Scholar
• Hyers , DH and Ulam , SM . 1952 . Approximately convex functions . Proceedings of the American Mathematical Society , 3 : 821 – 828 .
   Web of Science ®Google Scholar
• Kisielewicz , M . 1991 . Differential Inclusions and Optimal Control , Warszawa–Dordrecht : Kluwer Acad. Publ. and Polish Sci. Publ. .
   Google Scholar
• Krylov , NV . 1980 . Controlled Diffusion Processes, Applications of Mathematics , New York-Berlin : Springer Verlag .
   Google Scholar
• Nikodem , K and Wasowicz , S . 1995 . A sandwich theorem and Hyers–Ulam stability of affinne functions . Aequationes Mathematicae , 49 : 160 – 164 .
   Google Scholar
• Øksendal , B . 1998 . Stochastic Differential Equations, an Introduction with Applications, , 5th , Berlin : Springer Verlag .
   Google Scholar
• Phelps , RR . 1989 . Convex Functions, Monotone Operators and Differentiability , Berlin–Heidelberg–New York : Springer Verlag .
   Google Scholar
• Rishel , RW and Fleming , WH . 1975 . Deterministic and Stochastic Optimal Control, Applications of Mathematics , Berlin-New York : Springer Verlag .
   Google Scholar
• Rockafellar , RT and Wets , RJ-B . 1998 . Variational Analysis , Berlin–Heidelberg–New York : Springer Verlag .
   Google Scholar
• Tolstonogov , AA . 1986 . Differencialnye vklucenja v Banachovom prostranstve, Izdatelstvo Nauka, Sibirskoe Otdelene . Novosibirsk , (in Russian)
   Google Scholar