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Hyers–Ulam Stability for a First-Order Linear Proportional Nabla Difference Operator

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Frontiers in Functional Equations and Analytic Inequalities

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Abstract

The Hyers–Ulam stability (HUS) of a certain first-order proportional nabla difference equation with a sign-alternating coefficient is established. For those parameter values for which HUS holds, an HUS constant is found, and in special cases it is shown that this is the minimal such constant possible. A 2-cycle solution and a 4-cycle solution are shown to not have HUS.

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Author information

Authors and Affiliations

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

    Douglas R. Anderson

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  1. Douglas R. Anderson
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Correspondence to Douglas R. Anderson .

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Editors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA

    George A. Anastassiou

  2. Pedagogical Department E. E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens, Athens, Greece

    John Michael Rassias

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Anderson, D.R. (2019). Hyers–Ulam Stability for a First-Order Linear Proportional Nabla Difference Operator. In: Anastassiou, G., Rassias, J. (eds) Frontiers in Functional Equations and Analytic Inequalities. Springer, Cham. https://doi.org/10.1007/978-3-030-28950-8_15

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