No abstract

Let Ω be a convex open set of C , and let X be a complex Banach space. Suppose that p: Ω → C and q: Ω → X are holomorphic. We give sufficient conditions in order that the first order linear differential equation f (z) + p(z)f (z) + q(z) = 0 for X-valued holomorphic mapping f : Ω → X has the Hyers-Ulam stability.

No abstract

A new refinement of the classical arithmetic mean and geometric mean inequality is given. Moreover, a new interpretation of the classical mean is given and this refinement theorem is generalized.

Let P (z) be a polynomial of degree n with complex coefficients and consider the n-th order linear differential operator P (D). We show that the equation P (D)f = 0 has the Hyers-Ulam stability, if and only if the equation P (z) = 0 has no pure imaginary solution.