The Analysis Of Iteration For The Nonlinear Operators Under The Condition Of H(?)lder Continuous Or Nondifferential

This paper mainly study the convergence and error estimate for the nonlinear oper-ators,under the Holder continuous or non-differential condition. We improve the result of Hernandez and derive milder condition. The paper consists of three chapters.The first chapter gives some introductions on the background of the research for Newton-like iteration and the convergence conditions in common use.The main results of this paper are listed at the last.The second chapter investigates the convergence of Newton's iteration under the condition of Holder continuous.Base ourselves on the result of Hernandez,take full advantage of the information of the center Holder continuous condition, then we achieve milder condition,wider region for the uniqueness.and keep the convergence order with 1 + λ. At the last,we propose an example for the compare between our results and Hernandez's.The third chapter considers convergence of Newton-like iteration for the non-differential operator.Devide the non-differential operator into two parts:differential part H and the non-differential part G,make use of the modified iteration formula used by Hernandez,we analyze the convergence of the iteration.Compared with the result of Hernandez,our theorems need milder condition and derive better formula for error estimate.