The Convergence Theorems Of Iteration Methods For Nonlinear Equations And Convergence Rate Estimate

In recent years, the convergence of iteration processes has been studied extensively by many authors, including Mann iteration and Ishikawa iteration processes as the most important cases. However, the previous conclusions depend on special geometric properties and the strict conditions. Moreover, those results do not provide convergence rate estimate. Inspired by these facts, we suggest the new strongly convergence theorems of iteration methods for accretive operator equations and give the convergence rate estimate. The results in this paper relax the restrictions of the discussed space and lessen the conditions, so, our results improve and extend the relevant results in the more general setting. Mann iteration and Ishikawa iteration can all be viewed as special cases of the theorems in this paper. On the other hand, we represent an extension as well as refinement of nonlinear accretive operator theory and fixed point theory.