Stability Theorems for Solutions to the Optimal Inventory Equation

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Abstract
In a previous paper, [1] it was shown that a solution, f(x) will exist for the optimal inventory equation (where f(y − z) = f(0), y < z) provided: 1.g(x) ≧ 0, x ≧ 0; 2.0 < a < 1; 3.h(x) is monotonically nondecreasing, h(0) = 0; 4.F is a distribution function on [0, ∞);(In [1], 1–4 were denoted collectively as (A).)and either 5a.g(x) is continuous for all x ≧ 0; 5b.limx→∞g(x) = ∞; 5ch(x) is continuous for all x > 0 (Theorem 2 of [1]);or 6.g(x) is uniformly continuous for all x ≧ 0 (Theorem 3 of [1]).

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