Skip to main content
SpringerLink
Log in

Correction to: On the Unique Solvability of the Absolute Value Equation

  • Forum
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In this note, we give the two counterexamples for two unique solvability conditions that appeared in the published paper by Wu et al. (J Optim Theory Appl 169:705–712, 2016).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. For \(x \in {\mathbb {R}}^{n}\) sign(x) denotes a vector with components equal to \(-1\), 0 or 1 depending on whether the corresponding component of x is negative, zero or positive. The diagonal matrix D = diag(sign(x)) denotes a diagonal matrix corresponding to sign(x).

References

  1. Achache, M., Anane, N.: On unique solvability and Picard’s iterative method for absolute value equations. Bull. Transilv. Univ. Bras. III: Math. Comput. Sci. 1, 13–26 (2021)

    MathSciNet  Google Scholar 

  2. Mangasarian, O.L., Meyer, R.R.: Absolute value equations. Linear Algebra Appl. 419, 359–367 (2006)

    Article  MathSciNet  Google Scholar 

  3. Wu, S.L., Guo, P.: On the unique solvability of the absolute value equation. J. Optim. Theory Appl. 169, 705–712 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The research work of Shubham Kumar was supported by the Ministry of Education, Government of India, through Graduate Aptitude Test in Engineering (GATE) fellowship registration No. MA19S43033021.

Author information

Authors and Affiliations

  1. Department of Mathematics, PDPM-Indian Institute of Information Technology, Design and Manufacturing Jabalpur, Jabalpur, Madhya Pradesh, India

    Shubham Kumar

Authors
  1. Shubham Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shubham Kumar.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumar, S. Correction to: On the Unique Solvability of the Absolute Value Equation. J Optim Theory Appl 200, 891–893 (2024). https://doi.org/10.1007/s10957-023-02357-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-023-02357-3

Keywords

Mathematics Subject Classification

Search

Navigation