The weighted vertical linear complementarity problem on Euclidean Jordan algebra

In this article, we first introduce the weighted vertical linear complementarity problem (wVLCP) on a general Euclidean Jordan algebra, and we then study the boundedness and existence of solutions to the wVLCP by introducing the concept of \({\textbf{R}}'_0\) ${\mathbf{R}}_0^{\prime }$ , \({\textbf{R}}'\) ${\mathbf{R}}^{\prime }$ and \({\mathbf {P'}}\) ${\mathbf{P}}^{\prime }$ -pair properties for a pair of linear transformations. Finally, we present a uniqueness result for wVLCP on the Euclidean space \(\mathbb {R}^n\) ${\mathbb{R}}^n$ .