Hyers--Ulam Stability for Discrete Time Scale with Two Step Sizes

TL;DR

This paper investigates the Hyers--Ulam stability of first-order linear dynamic equations on a specific discrete time scale with two alternating step sizes, analyzing stability constants and their minimality.

Contribution

It provides new insights into the stability constants for equations on a two-step size time scale with sign-changing exponential functions.

Findings

HUS is established for the considered dynamic equations.

The paper discusses the HUS constant and the possibility of minimal constants.

Results are specific to a time scale with two alternating step sizes.

Abstract

We clarify the Hyers--Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, in the case of a specific time scale with two alternating step sizes, where the exponential function changes sign. In particular, in the case of HUS, we discuss the HUS constant, and whether a minimal constant can be found.