Common Hermitian solutions to some operator equations on Hilber C∗-modules

We establish necessary and sufficient conditions for the existence of the general common Hermitian solution to the equations for adjointable operators between Hilbert C∗-modules, and present an expression for the common Hermitian solution to the equations in terms of Moore–Penrose inverse of operators when the solvability conditions are satisfied. The findings of this paper extend some known results in the literature.