On Hermitian solutions of the reduced biquaternion matrix equation ( AXB,CXD ) = ( E,G )

This paper aims to consider the Hermitian solutions of reduced biquaternion matrix equation (AXB,CXD)=(E,G), where X is an unknown reduced biquaternion Hermitian matrix, and A, B, C, D, E, G are known reduced biquaternion matrices with suitable size. The main work is to establish necessary and sufficient conditions for the existence of a solution and a solution formula.