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

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.

کلیدواژه ها:

Absolute value equation ، Necessary condition ، Sufficient condition ، Unique solution