| Abstract: |
| In this talk, we deal with Hyers--Ulam stability of the first-order nonhomogeneous linear difference equation $\Delta_hx(t)-ax(t) = f(t)$ on $h\mathbb{Z}$, where $\Delta_hx(t) = (x(t+h)-x(t))/h$ and $h\mathbb{Z} = \{hk|\,k\in\mathbb{Z}\}$ for the constant stepsize $h>0$; $a$ is a real number; $f(t)$ is a real-valued function on $h\mathbb{Z}$. The purpose of this talk is to answer the question `how does the stepsize influence the best HUS constant for the linear equation on $h\mathbb{Z}$?`. |
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