On Ulam Stability with Respect to 2-Norm

Abstract

The Ulam stability of various equations (e.g., differential, difference, integral, and functional) concerns the following issue: how much does an approximate solution of an equation differ from its exact solutions? This paper presents methods that allow to easily obtain numerous general Ulam stability results with respect to the 2-norms. In four examples, we show how to deduce them from the already known outcomes obtained for classical normed spaces. We also provide some simple consequences of our results. Thus, we demonstrate that there is a significant symmetry between such results in classical normed spaces and in 2-normed spaces.

Remarks on Approximate Solutions to Difference Equations in Various Spaces

“…Moreover, it would be interesting to improve and complement the results presented here, but also investigate similar outcomes for other equations (including differential, functional and integral equations). In connection with this last issue, we would like to draw the attention of interested readers to the methods presented in [64] and to the outcomes in publications [10,[27][28][29][30][31][32] (that were proven mainly in the case of normed spaces).…”