Ishikawa-type iterative solution of m-accretive operator equation and its stability in arbitrary Banach spaces

Abstract

Let X be a Banach space. Suppose that A : X → X is a Lipschitz accretive operator and x+Ax = f is a nonlinear equation. The objective of this note is to discuss simultaneously the existence and uniqueness of solution of the equation, its convergence, convergence rate estimate and stability of Ishikawa-type iterative procedure. If iterative parameters be selected suitably, then the iterative procedure converges strongly to unique solution and the iterative process is stable.