On Mann Iteration And Ishikawa Iteration With Errors For Accretive Operator And The Equivalence

The iterations of accretive mappings include four kinds, which are Mann iteration, Ishikawa iteration, Mann iteration with errors and Ishikawa iteration with errors. Among these iterations Mann iteration is the most simple and appreciate. In this paper, we study the equivalence of the above four iterations about strongly accretive operators,φ-strongly accretive operators and uniformlyφ-accretive operators in the common spaces—Banach spaces. Our results greatly generalize and extend some recent main results. Moreover, we-also discuss the convergence of the perturbed equation. And at the same time, we construct a new iterative process and discuss its convergence. This is the latest result recently.This paper includes four sections. The first section is introduction; The second section is preliminaries; The third section discusses the equivalence of the following types iterations: uniformlyφ-accretive mappings,φ-strongly accretive mappings andφ-pseudocontractive mappings. The fourth section discusses the iterations of perturbed equations on strongly accretive operator and compact perturbed equations.