Hyers–Ulam Stability for Quantum Equations of Euler Type

Abstract EN

Many applications using discrete dynamics employ either q-difference equations or h-difference equations.

In this work, we introduce and study the Hyers–Ulam stability (HUS) of a quantum (q-difference) equation of Euler type.

In particular, we show a direct connection between quantum equations of Euler type and h-difference equations of constant step size h with constant coefficients and an arbitrary integer order.

For equation orders greater than two, the h-difference results extend first-order and second-order results found in the literature, and the Euler-type q-difference results are completely novel for any order.

In many cases, the best HUS constant is found.