Ulam–Hyers stability of dynamic equations on time scales via Picard operators

摘要

In this paper we study the Ulam–Hyers stability of some linear and nonlinear dynamic equations and integral equations on time scales. We use both direct and operatorial methods and we propose a unified approach to Ulam–Hyers stability based on the theory of Picard operators (see [28], [33]). Our results extend some recent results from [24], [25], [8], [14], [13], [5], [6] to dynamic equations and are more general than the results from [1].The operatorial point of view, based on the theory of Picard operators, allows to discuss the Ulam–Hyers stability of many types of differential- and integral equations on time scales and also to obtain simple and structured proofs to the existing results, but as we point out at our final remarks there are also a few disadvantages.