Ishikawa Iterative Approximations of Solutions to Equations Involving Accretive Operators

Abstract:

      Let X be an arbitrary real Banach space and T : X →X be a Lipschitz continuous accretive operator. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation x+Tx =f. Moreover, our result provides a general convergence rate estimate for the Ishikawa iterative sequence. Utilizing this result, we show that if T : X →X is a Lipschitz continuous strongly accretive operator, then the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation Tx=f.