Behavior of the positive solutions of fuzzy max-difference equations.
We consider real valued functions defined on a subinterval of the positive real axis and prove that if all of ’s quantum differences are nonnegative then has a power series representation on . Further, if the quantum differences have fixed sign on then is analytic on .
In rings of formal power series in several variables whose growth of coefficients is controlled by a suitable sequence (such as rings of Gevrey series), we find precise estimates for quotients F/Φ, where F and Φ are series in such that F is divisible by Φ in the usual ring of all power series. We give first a simple proof of the fact that F/Φ belongs also to , provided is stable under derivation. By a further development of the method, we obtain the main result of the paper, stating that...