On the maximum principle for optimal control processes described by Hammerstein integral equations with weakly singular kernels
Let C(Ω) be the algebra of all complex-valued continuous functions on a topological space Ω where C(Ω) contains unbounded functions. First it is shown that C(Ω) cannot have a Banach algebra norm. Then it is shown that, for certain Ω, C(Ω) cannot possess an (incomplete) normed algebra norm. In particular, this is so for where ℝ is the reals.
Let L(Φ) [0, +∞) be the Orlicz function space generated by N-function Φ(u) with Luxemburg norm. We show the exact nonsquare constant of it when the right derivative φ(t) of Φ(u) is convex or concave.