On uniformly continuous Nemytskij operators generated by set-valued functions

Let I = [0, 1], let Y be a real normed linear space, C a convex cone in Y and Z a real Banach space. Denote by clb(Z) the set of all nonempty, convex, closed and bounded subsets of Z. If a superposition operator N generated by a set-valued function F : I × C → clb(Z) maps the set H _α (I, C) of all Hölder functions ${varphi : I to C}Let I = [0, 1], let Y be a real normed linear space, C a convex cone in Y and Z a real Banach space. Denote by clb(Z) the set of all nonempty, convex, closed and bounded subsets of Z. If a superposition operator N generated by a set-valued function F : I × C → clb(Z) maps the set H _α (I, C) of all H?lder functions j: I ? C{varphi : I to C} into the set H _β (I, clb(Z)) of all H?lder set-valued functions f: I ? clb(Z){phi : I to clb(Z)} and is uniformly continuous, then

F(x,y)=A(x,y) text+* B(x),       x ? I, y ? CF(x,y)=A(x,y) stackrel{*}{text{+}} B(x),qquad x in I, y in C
Keywords:
本文献已被 SpringerLink 等数据库收录！