On Continuous Solutions of a Functional Equation.
This paper discusses continuous solutions of the functional equation φ[f(x)] = g(x,φ(x)) in topological spaces.
A continuous multifunction F:[a,b] → clb(Y) is *-concave if and only if the inclusion holds for every s,t ∈ [a,b], s < t.
We study the integral representation of potentials by exit laws in the framework of sub-Markovian semigroups of bounded operators acting on . We mainly investigate subordinated semigroups in the Bochner sense by means of -subordinators. By considering the one-sided stable subordinators, we deduce an integral representation for the original semigroup.