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《Acta Analysis Functionalis Applicata》 2009-01
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Trapezium Newton′s Method for Nonlinear Operator Equations

XUE Ya-ping, WU Kai-su, LIU Xiao-jing Department of Mathematics and Information Science, Beijing University of Chemical Technology, Beijing 100029, China  
The main object of this paper is to investigate the solution of nonlinear operator equation F(x)=0 in Banach space. First, we generalize the trapezium formula about numerical integral of real function to the Bochner integral of nonlinear functional so that we obtain the trapezium formula of Bochner integral. Then we use the formula to construct modified scheme of Newton′s iterative method so as to obtain trapezium Newton′s method. Futhermore ,we proved its convergence under α-criterion of weak conditions by means of majorizing function.
【Fund】: 北京化工大学青年科学基金(QN0622)
【CateGory Index】: O242.23
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