Hyers–Ulam stability for quantum equations


We introduce and study the Hyers–Ulam stability (HUS) of a Cayley quantum (q-difference) equation of first order, where the constant coefficient is allowed to range over the complex numbers. In particular, if this coefficient is non-zero, then the quantum equation has Hyers–Ulam stability for certain values of the Cayley parameter, and we establish the best (minimal) HUS constant in terms of the coefficient only, independent of q and the Cayley parameter. If the Cayley parameter equals one half, then there is no Hyers–Ulam stability for any coefficient value in the complex plane.

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The authors would like to thank the referees for reading carefully and giving valuable comments to improve the quality of the paper. The second author was supported by JSPS KAKENHI Grant Number JP20K03668.

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Correspondence to Douglas R. Anderson.

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Anderson, D.R., Onitsuka, M. Hyers–Ulam stability for quantum equations. Aequat. Math. (2020). https://doi.org/10.1007/s00010-020-00734-1

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  • Stability
  • Hyers–Ulam
  • Quantum calculus
  • Best constant

Mathematics Subject Classification

  • 39A06
  • 39A13
  • 39A30
  • 34N05