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Research Article | Open Access

On Ulam stability of a second order linear difference equation

Delia-Maria Kerekes( ), Bianca Moșneguțu, Dorian Popa
Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului St., 400114, Cluj-Napoca, Romania
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Abstract

In this paper we obtain some Ulam stability results for the second order and the third order linear difference equation with nonconstant coefficients in a Banach space. The main idea of the approach is to decompose the second order linear difference equation in a Riccati difference equation and a first order difference equation. In this way we extend some results for linear difference equations with constant coefficients and for linear difference equations with periodic coefficients.

Keywords

Ulam stabilityapproximate solutionlinear difference equationRiccati difference equationnonconstant coefficients
CLC number: Primary 39A30, Secondary 39B82

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 20254-20268
DOI: 10.3934/math.20231032

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Cite this article:
Kerekes D-M, Moșneguțu B, Popa D. On Ulam stability of a second order linear difference equation. AIMS Mathematics, 2023, 8(9): 20254-20268. https://doi.org/10.3934/math.20231032

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Received: 23 March 2023
Revised: 13 May 2023
Accepted: 19 May 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)