b =lim ray / - -, b E So we can extract from the sequence (f.) a sequence (..) such that (m) (P),2%E*)-converges to a functions. We have, for each te[0,1], 16 (1) = limu.) re 4 -"(s)ds + () (t - 5)-f(s)ds + (1). () Thus c = . This means that my converges in CE([0,1]) to use and shows the compactness of X'in CE([0,1]). At this point, it is worth to mention that the sequence (w-D-_)) converges to w-D-- () in E, for E endowed with the strong topology by using the o(P.,20 E*)-convergence of () and the norm compactness of x(s)ds. Remark. -e-s) dependence of the mappinys f u and f w-De-lus on the convex (P. E*)-compact sets. This fact has some importance in further applications. (2) It is worth to mention that {w-D-tus:f est is also compact in C:((0,1). Now we proceed to the existence of solutions in W/([0,1]) for the(FDI) w-Du(t) F(t,u(t), w-Da-\u(t), 1 [0, 1] (0) = 0, w-D- (0) = b multifunction et (0,0) - E be a convex compact valued mapping satisfying (1) Fis scalarly C. ([0,1]) B(E) B(E)-measurable, i.e., for each x* E*, the scalar function 8*(** F(.....)) is L. (0,1)B(E) B(E)-measurable, (2) The mapping F(t,...) is scalarly upper semicontinuous, that is, for each 1 [0, 1] and for each x* E, the scalar function 8*(3*,F(t,...)) is upper semiconicons on ExE, (3) F(t, x,y) C X(t) for all (t.x, y) = [0, 1] Then the w0, 1])-solutions set to the (FDI) w-Du(t) F(t.u(),w-D-! (0) = 0, w-D-(O) = b