Block representations of the generalized Drazin inverse

Additive properties of G-Drazin inverse of linear operators

“…We apply our results to establish new conditions under which M has g-Drazin inverse. Our results contain many known results, e.g., [5] and [11].…”

“…We always use A d to stands for the set of all g-Drazin invertible a ∈ A. The g-Drazin inverse of operator matrix has various applications in singular differential equations, Markov chains and iterative methods (see [1,2,3,5,6,7,9,11,12]). The motivation of this paper is to explore new additive properties of g-Drazin inverse for linear operators in Banach spaces.…”

The representations of the g-Drazin inverse in a Banach algebra

“…Here, M is a bounded linear operator on X ⊕ X. This problem has been expensively studied by many authors (see [1,2,6,7,9]. We then apply our results to establish new conditions under which M has g-Drazin inverse.…”

On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus

“…in which a D γ x and x D γ are (11) and (12) for m = 2. According to [50], the first-order time derivative at the point t = t j is approximated by the second-order backward difference formula:…”

“…This definition does not have flexibility in the rings and semi-groups of associations but commutes with the element. The importance of this type of inverse and its calculation was later discussed by Wilkinson [10], and several researchers proposed direct or iterative methods for calculating the solution of this problem [11][12][13][14]. In this paper, a characterization of the Drazin inverse in the scope of fractional calculus is investigated.…”