On the unique solution of a class of absolute value equations $ Ax-B|Cx| = d $

Hongyu Zhou; Shiliang Wu; Hongyu Zhou; Shiliang Wu

doi:10.3934/math.2021517

AIMS Mathematics

2021, Volume 6, Issue 8: 8912-8919. doi: 10.3934/math.2021517

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On the unique solution of a class of absolute value equations $ Ax-B|Cx| = d $

Hongyu Zhou ¹,
Shiliang Wu ^{2
,
,}

1.
School of Computer and Information Engineering, Anyang Normal University, Anyang, Henan 455000, China
2.
School of Mathematics, Yunnan Normal University, Kunming, Yunnan 650500, China

Received: 05 May 2021 Accepted: 09 June 2021 Published: 15 June 2021
MSC : 90C05, 90C30, 65F10

In this paper, a class of absolute value equations (AVE) $ Ax-B|Cx| = d $ with $ A, B, C\in \mathbb{R}^{n\times n} $ is considered, which is a generalized form of the published works by Wu ^[1], Wu and Shen ^[2] and Mezzadri ^[3]. Some conditions to guarantee the unique solution of the above AVE are gained. The corresponding results of the above published works are generalized.
- sufficient condition,
- unique solution,
- absolute value equation
Citation: Hongyu Zhou, Shiliang Wu. On the unique solution of a class of absolute value equations $ Ax-B|Cx| = d $[J]. AIMS Mathematics, 2021, 6(8): 8912-8919. doi: 10.3934/math.2021517

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Abstract

In this paper, a class of absolute value equations (AVE) $ Ax-B|Cx| = d $ with $ A, B, C\in \mathbb{R}^{n\times n} $ is considered, which is a generalized form of the published works by Wu ^[1], Wu and Shen ^[2] and Mezzadri ^[3]. Some conditions to guarantee the unique solution of the above AVE are gained. The corresponding results of the above published works are generalized.

References

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