In this paper, we generalize the upper bound in Varadhan’s Lemma. The standard formulation of Varadhan’s Lemma contains two important elements, namely an upper semicontinuous integrand and a rate function with compact sublevel sets. However, motivated by results from queueing theory, in this paper we do not assume that rate functions have compact sublevel sets. Moreover, we drop the assumption ...

This paper studies stochastic inventory problems with unbounded Markovian demands, ordering costs that are lower semicontinuous, and inventory/backlog (or surplus) costs that are lower semicontinuous with polynomial growth. Finite horizon problems, stationary and nonstationary discounted cost in nite horizon problems, and stationary long-run average cost problems are addressed. Existence of opt...

Let σ be a positive number and Cσ := C([−σ, 0], R) the Banach space of continuous functions from [−σ, 0] into R and let T (t) be the operator from C([−σ, T ], R) into Cσ, defined by (T (t)x)(s) := x(t + s), s ∈ [−σ, 0]. We prove the existence of solutions for functional differential inclusion(differential inclusions with memory) x′ ∈ F (T (t)x) + f(t, T (t)x) where F is upper semicontinuous, co...

If (X, τ) is a topological space, we denote by τs the topology on X whose members are the sets A ⊆ X such that X \A is sequentially τ -closed. Clearly, τs is stronger than τ . We note that a function f : X → R is sequentially τ -lower semicontinuous if and only if it is τs-lower semicontinuous. We also recall that a real function φ on a convex subset C of a vector space is said to be quasi-conc...

In this note we present a new treatment of the pointfree version of the semicontinuous quasi-uniformity based on the new tool of the ring of arbitrary (not necessarily continuous) real-valued functions made available recently by J. Gutiérrez Garćıa, T. Kubiak and J. Picado [Localic real functions: a general setting, Journal of Pure and Applied Algebra 213 (2009) 1064-1074]. The purpose is to sh...