such as was treated in the previous papers [3] and [4]. However, we shall show that we can replace the strong continuous differentiability of A(t)A(s)~ by its Holder continuity by means of a slight change of the proof. It is quite clear that the differentiability of A(t)A(s)~ is not necessary for the construction of the formal fundamental solution U(t, s) of (0. 1'). In the previous papers, how...

The well-known finite-dimensional first-order open mapping theorem says that a continuous map with a finite-dimensional target is open at a point if its differential at that point exists and is surjective. An identical result, due to Graves, is true when the target is infinite-dimensional, if “differentiability” is replaced by “strict differentiability.” We prove general theorems in which the l...

We consider the single-leg airline revenue management problem in continuous time with Poisson arrivals. Earlier work on this problem generally uses the Hamilton-Jacobi-Bellman equation to find an optimal policy whenever the value function is differentiable and is a solution to this equation. In this paper, we employ a different probabilistic approach, which do not rely on the smoothness of the ...

In this paper optimal control problem of fuzzy linear time invariant systems is considered. Determining of system optimal input with minimizing quadratic integral criterion by using Pontryagin Minimum Principle will make the Fuzzy Partial Differential Equations [FPDEs] system solve the problem. The quality of obtaining system optimal input by solving the FPDEs system has been studied based on n...

This paper is concernedwith a periodic system dependent on parameter. We study differentiability with respect to parameters of the periodic solution of the system. Applying a fixed point theorem and the results regarding parameters for C0-semigroups, we obtained some convenient conditions for determining differentiability with parameters of the periodic solution. The paper is concluded with an ...

Abstract. Differentiability properties of optimal value functions associated with perturbed optimization problems require strong assumptions. We consider such a set of assumptions which does not use compactness hypothesis but which involves a kind of coherence property. Moreover, a strict differentiability property is obtained by using techniques of Ekeland and Lebourg and a result of Preiss. S...