In this paper, we establish several relationships between \(m\) -EP operator and the DMP and MPD inverses of an operator. We prove that an operator \(T\) is \(m\) -EP if and only if it is Drazin invertible and satisfies \((T^{D,\dagger })^n = (T^{\dagger ,D})^n= (T^{D})^n \) for all integers \(n \ge 1\) . We also provide characterizations of \(m\) -EP operator in terms of their adjoint and matrix representation. In addition, we introduce two new classes of operators associated with the DMP and MPD inverses, which we call \(m\) -DMP and \(m\) -MPD operators, respectively. Finally, we show that an operator \(T\) is \(m\) -EP if and only if it is both \(m\) -DMP and \(m\) -MPD.
