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<p>This paper investigates the conditions that guarantee unique solvability and unsolvability for the generalized absolute value equations (GAVE) of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Ax - B \vert x \vert = b\)</EquationSource> </InlineEquation>. We present new solvability criteria that go beyond existing spectral and singular value conditions. These conditions are further extended to the absolute value matrix equations (AVME) <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(AX - B \vert X \vert =F\)</EquationSource> </InlineEquation>, thereby broadening their applicability. In addition, we give the possible revised version of the unique solvability conditions for the two incorrect results that appeared in the published paper by Wu et al. (Appl Math Lett 76:195–200, 2018).</p>

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The Unique Solvability Conditions for the Generalized Absolute Value Equations

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Shubham Kumar,
  • Deepmala,
  • Shi-Liang Wu

摘要

This paper investigates the conditions that guarantee unique solvability and unsolvability for the generalized absolute value equations (GAVE) of the form \(Ax - B \vert x \vert = b\) . We present new solvability criteria that go beyond existing spectral and singular value conditions. These conditions are further extended to the absolute value matrix equations (AVME) \(AX - B \vert X \vert =F\) , thereby broadening their applicability. In addition, we give the possible revised version of the unique solvability conditions for the two incorrect results that appeared in the published paper by Wu et al. (Appl Math Lett 76:195–200, 2018).