Generalized Reflexive and anti-reflexive Solution for a system of equations

Abstract

In this article we find necessary and sufficient conditions for the generalized
reflexive and antireflexive solution of the system of equations $ax=b$ and $xc=d$ in a
ring with involution. As corollaries, among other results, we obtain some recent
results from (A. Daji\'c and J. Koliha, Linear Algebra Appl. (2008)), and Li Fanliang,
Hu Xiuyan and Zhang Lei, Acta Math. Scientia 28B(1) (2008)).