In this paper we construct a few iterative processes for computing {1, 2} inverses of a linear bounded operator, based on the hyper-power iterative method or the Neumann-type expansion. Under the suitable conditions these methods converge to the {1, 2, 3} or {1, 2, 4} inverses. Also, we specify conditions when the iterative processes converge to the Moore-Penrose inverse, the weighted Moore-Pen...
