The Jarratt method in Banach space setting
type: Item
instance of: scholarly article
title: The Jarratt method in Banach space setting
zbMATH Open document ID: 0809.65054
DOI: 10.1016/0377-0427(94)90093-0
author: Ioannis Konstantinos Argyros
author: D. Chen
author: Q. S. Qian
published in: Journal of Computational and Applied Mathematics
publication date: 1994-09-25T00:00:00Z
review text: Convergence and error estimates of the Jarratt iterative method \(y_ n= x_ n- F'(x_ n)^{-1} F(x_ n)\), \[ H(x_ n, y_ n)= F'(x_ n)^{-1} [F'(x_ n+\textstyle{{2\over 3}}(y_ n- x_ n))- F'(x_ n)], \] \(x_{n+1}= y_ n- {3\over 4} [I+ {3\over 2} H(x_ n, y_ n)]^{-1} H(x_ n, y_ n)(y_ n- x_ n)\), are given for solving nonlinear operator equations \(F(x)= 0\). Here \(F\) maps a convex subset of \(X\) into \(Y\) which are Banach spaces. A quadratic integral equation is discussed as an example.
reviewed by: Zhen Mei
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 641401
zbMATH Keywords: Jarratt iterative method
zbMATH Keywords: nonlinear operator equations
zbMATH Keywords: Banach spaces
zbMATH Keywords: quadratic integral equation
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90093-0
OpenAlex ID: W1989330245
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description: scientific article; zbMATH DE number 641401