Journal of the
Korean Mathematical Society JKMS

The existence of a unique local generalized solution for the abstract
functional evolution problem of the type
$$x'(t)+A(t, x_t) x(t) \ni G(t, x_t), \ t\in [0, T], \quad
x_0=\phi\tag{FDE:$\phi$}$$
in a general Banach spaces is considered. It is shown that
(FDE:$\phi$) could be considered with well-known fixed point theory
and recent results for the functional differential equations involving
the operator $A(t)$.

Keywords: subharmonic function, smooth function, harmonic measure, norm inequality

MSC numbers: 34K30, 47H20, 34L20