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Hyers–Ulam Stability and Best Constant for Cayley h-Difference Equations

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Abstract

A Cayley h-difference equation uses the forward-difference operator with step size h and then some proportion of the function value and the advanced function value. For such an equation with a complex constant coefficient, we establish that the equation exhibits instability along a certain circle, but is Hyers–Ulam stable inside and outside that circle; the circle becomes infinite and coincides with the vertical imaginary axis when the proportionality is equal. In the case of Hyers–Ulam stability, the best constant is found explicitly. The theory is also explained in terms of radial solutions, and an example is illustrated.

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Funding

JSPS KAKENHI Grant Number JP17K14226 supports the second author.

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Authors and Affiliations

  1. Department of Mathematics, Concordia College, Moorhead, MN, 56562, USA

    Douglas R. Anderson

  2. Department of Applied Mathematics, Okayama University of Science, Okayama, 700-0005, Japan

    Masakazu Onitsuka

Authors
  1. Douglas R. Anderson
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  2. Masakazu Onitsuka
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Correspondence to Douglas R. Anderson.

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Communicated by Pham Huu Anh Ngoc.

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Anderson, D.R., Onitsuka, M. Hyers–Ulam Stability and Best Constant for Cayley h-Difference Equations. Bull. Malays. Math. Sci. Soc. 43, 4207–4222 (2020). https://doi.org/10.1007/s40840-020-00920-z

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  • DOI: https://doi.org/10.1007/s40840-020-00920-z

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