Of a couple of relaxation iterative methods suited for matrices of bounded linear operators defined over banach spaces

By introducing matrices of linear bounded infinite-dimensional operators defined over some Banach spaces, and within the context of study, we make use of the definition of row strict diagonal dominance property to construct a generalization version of the Jacobi Under-Relaxation and the Successive Under-Relaxation iterative methods. The convergence analyses of the two new iterative methods are provided, and a numerical application to solve one Fredholm integral equation is presented to show the generalized methods' effectiveness compared with their conventional opponents.