Analysis of the Distance Between Successive Generalized Zeros of First-Order Linear Difference Equations with Several Variable Delays

This study examines the distances between consecutive generalized zeros of first-order difference equations with several variable delays. We develop new techniques to obtain the upper bounds for these distances. The results are not only new, but they also extend and improve several earlier contributions in this area. In particular, our analysis covers the case of nonmonotonic delay sequences, which, to the best of our knowledge, has not been previously investigated, even for the corresponding delay differential equations. To illustrate the effectiveness of our findings, three numerical examples will be presented.