Solvability of a nonlocal boundary value problem for linear functional differential equations

In the paper, the problem on the existence and uniqueness of a solution to the nonlocal problem u'(t) = L(u)(t) + q(t), u(a) = h(u) + c is considered, where l : C([a,b]; R) -> L([a,b]; R) and h : C([a,b]; R) -> R are linear bounded operators, q is an element of L([a,b]; R), and c is an element of R.