International Journal of Nonlinear Analysis and Applications

A note on different conditions of the unique solvability for the absolute value equation

Document Type : Review articles

Authors

1 Delhi Skill and Entrepreneurship University, Sector-9, Dwarka, New Delhi, India

2 Department of Applied Science, IIMT Engineering College Meerut, Uttar Pradesh, India

3 Mathematics Discipline, PDPM- Indian Institute of Information Technology, Design and Manufacturing, Jabalpur-482005, Madhya Pradesh, India

Abstract

In this study, we compare the different conditions which are used to detect the unique solvability of the absolute value equation (AVE) $Ax- B \vert x \vert =b$. Also, analyzing which condition is more suitable to use according to our problem and later, we will see the advantage and disadvantages of different unique solvability conditions. Further, we take an example where existing conditions are invalid to judge the unique solvability of the AVE.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 3
March 2024
Pages 371-375
  • Receive Date: 17 January 2023
  • Revise Date: 18 February 2023
  • Accept Date: 21 June 2023