Characterization of unique solvability of absolute value equations: an overview, extensions, and future directions

Shubham Kumar, Deepmala, Milan Hladík, Hossein Moosaei

Abstract: This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several generalizations, including generalized absolute value equations and matrix absolute value equations. Our survey encompasses known results as well as novel characterizations proposed in this study.